Vol 7 Chapter 4 (1/2)

The Fourth Question

Use :

1 + 3 + 5 + … + (2n-1)=n2①

When n is a natural number

Himeji Mizuki's answer

1 When n=1, equation ① is calculated as,

Left Hand Side = 1

Right Hand Side = 1

2 assu that n=k is valid,

1 + 3 + 5 + … + (2k-1)=k2②

When n=k+1, the left hand side of ① is written as

1 + 3 + 5 + … + (2k-1)+(2k+1)

=k2 + (2k+1) (Obtained from equation ①)

=(k+1)2

In other words,

1 + 3 + 5 + … + (2k-1)+(2k+1)

=(k+1)2

① is valid when n=k+1

From 1 and 2, equation ① is valid for all values on n

Teacher's comment

That's correct In mathematical induction, you need to prove that n=1 is valid Also, when assu that n=k is valid, you have to deduce that n=k+1 is valid In this question, the key is that n is a natural nuet to put that n=1, so do take note when answering

Tsuchiya Kouta's answer

”I'll prove here that ① is correct - Tsuchiya Kouta”

Teacher's comment

Even if you try to sneak through by writing it in a style of a thesis, it's useless The question h ' that n=k, please write the equation that n=k+1 is valid

Yoshi+ Akihisa's answer

”My judgment can hold”

Teacher's comment

”Please use an assumption”

“Oh! Akihisa, you're back”

“Been tough on you, Akihisa”

“Welcome back”

“Ah, mn, I'm back”

As I finish the replenishment tests and return to the middle of the sports arena, Hideyoshi+ and the rest kindly receivethe left behind a bit But whether on or lost, I still wished to see it through with everyone

Thinking about this, my eyes turn to the class F rest area that's bounded by rope At thisa strange box and arguing What are they doing?

“PLEASE LET ME BE THE LUCKY GUY!”

“STOP YAPPING AND START DRAWING! THERE ARE PEOPLE BEHIND!”

“I GOT IT, I GOT IT! WHY ARE YOU GUYS SO ANXIOUS! ALRIGHT, IT'S THIS ONE—damn IIIIIITTTTT!!!”

“““NICE! CRY YOUR WAY HOME!!!”””

“Eh, what are they doing?”

I asked Yuuji who's beside me Several classmates of mine seem to be dejected and unhappy Why is that?

“H a lucky draw”

“I know that I just want to knohy they're doing it”

“Oh The next event is the 2-people-3-legged race The draw's to decide who goes ho”

“Heh~so that's how it is”

It's true that the choosing of partners in the 2-people-3-legged race is crucial More than one's own ability, theis for both sides to be able to co-ordinate together

“What's wrong, Akihisa? You're pretty calm”

Hideyoshi+ asked me with a puzzled look, but there's no reason for me not to remain calm

“Because it doesn't irls will be separated anyway--”

“This is a mixed event”

“No problems at all SUMMON!”

GO, MY SUMMONED BEAST! KILL THOSE GUYS FOR ME!!

“CALM DOWN, YOU IDIOT! DO YOU THINK YOU CAN SUMMON WITHOUT A TEACHER'S PERMISSION?”

“I CAN'T CALM DOWN AT ALLLL!! WHO IS IT? WHO'S THAT LUCKY GUY WHO GOT THE LUCKY NUMBER?”

“Relax, it's not decided yet”

“Eh? Really?”

“If that were the case, ouldn't be quarreling like this”

“Ah, you're right”

Luckythe key to winning the 2-people-3-legged race is to not get anxious and ether If there's any traitor ould do such a great thing to the girls, that guy will be massacred by the FFF

“I see That's why everyone's praying”

“That's the case”

Everyone's praying before they stand in front of the box, putting their hands together and praying

“But, to think that Hied race with the guys as well Yuuji, did you say so to them?”

Looking over there, the other girls seeender Himeji-san and Minami probably did that because there are only 3 people, Himeji-san, Minami and Hideyoshi+ and can't leave someone out?

Hearing ives a 'really, you' look

“What idiotic words are you saying? I would wish for guys and girls to be in different groups”

“Eh? Why—oh ya, I understand You'll be killed if so”

“Good that you can understand”

Once Kirishi+irl, no matter how far Yuuji is, she would install so as 'iirl-in-love's dictionary—everyone knows that

“More than that, I feel that the baseball tournament's more important”

“I agree”

Yuuji and Muttsurini nod their heads These people have already turned into Asura just to get their confiscated A-books They would prefer theback their A-books 10,000 tilory

“If that's the case, the next ht?”

The middle (first) sports arena is used to hold the sports meet, and the second arena that's located behind the school compound was used to hold our second-year baseball tourna the 3rd years later

“They haven't finished yet It's extra innings”

“Oh, if we're successful, we get a walk over”

Due to the tis If they can't win, the match will be decided as a tie It sounds nice, but both sides can't progress on If that's really the case, we can take the next

“Anyway, let's check the next ay, raphy”

Yuuji took out the schedule to check These are all basic, normal subjects

“No health education”

Muttsurini sounded rather lonely when he said that as he glanced at the schedule in Yuuji's hand Like what Muttsurini says, there's no health education for every match

“If that's the case, do you want to take part in the sports meet event, Muttsurini?”

“You're right We'll do that for the second round”

“I got it”

To think that Muttsurini would actually leave the frontlines However, since there's no health education in the next few matches, it can't be helped Besides, Muttsurini's other subjects are worse than me

“Then we should readjust the batting order and the defensive alignments The first one is awa handle the second That guy seems like he can really bunt”

“Then what about me? I can't handle maths”

“You can't handle maths 'too' Besides, even if we leave you at the back few batters, your biology scores are atrocious, so I ood if you can really bunt If you're successful, we should be able to get 1 point”

“Mn, got it”

Yuuji decided our batting order and defensive positioning

Just when Yuuji and I are discussing--

“Well, erm, Akihisa-kun”

A voice called me from behind This voiceHimeji-san?

“H?”

Turning around, I see that Hi really serious What's going on?

“It's not really so”

“WellAkihisa-kun, what's your number?”

“Eh? You're asking me for my number”

Ah, should be the batting order, right? As expected of His She would actually check the defensive position and batting order Though she's not really good at understanding sports, it see about this match

Uu,order

“I'm 3 Number three”

““WAH!!””

After I answered that, Himeji-san and Mina order weird?

“UuuI know the chances are sliht that it could be possible”

“That's too the one chance to stick on This is a rare chance”

Both of the onto a little piece of paper each as they becried

“AH~so you're talking about that Don't worry, you two, Akihisa was just talking about the batting order He hasn't drawn the nued race”

Yuuji said to the them

““Eh?””

Himeji-san and Minao, lifted their heads up at the sa the 2-persons-3-legged race?

“Oh ya I forgot all about that Got to take one number!”

Who can take it if those guys take the wonderful opportunity to be with the girls!?

“Ah, thatAkihisa-kun!”

“Wait, Aki!”

As I was about to go for the box of numbers, Himeji-san and Minami suddenly stopped me Uuif I don't hurry up, my happiness will be taken away

“What? Is there so?”

“No Wewellwhat should I sayI'm 7”

“My number's 6”

Hierly 7 and 6? I see So I'll strike jackpot if I get these nuht--

““(PLEASE) DON'T DRAW THIS NUMBER!””

Seems like they really hate me

“I, I got itthen, I'll draw one number then”

“I say, you two Those words may have already caused Akihisa to misunderstand”

“Be, because it's Akihisa-kunif we say to him 'please draw this number'--”

“That, that's right! When that happens, it will become the opposite of ish for For soet Saka”

“Really, it's been tough on you two”

Sigh, though I never had ood draay But I' awa-san, who's watching over the box

“Alright, Yoshi+, draw your fate”

“Uu, okay”

With Sugawa-san staring at me mysterious, I reach my hand into the box It'll be heaven if I can draw 6 or 7, so I have to do my best Uuokay, this one!

I immediately pull out the number The number written on the paper is--

“Ah, 6”

“KILL HIM!!!”

“““YES, HIEROPHANT!!!”””

“WHAT'S GOING ON? I GOT SURROUNDED!”

I haven't even said roup of people in black hoods surroundedout my number so openly like that, is it the end of me

“6, 6I see, so Aki will be with me”

“UuMinami-chan looks so happy”

“Do, do I? When do I look happy”

“You liar! I can see your face glowing”

“Uu”

“I think Minami-chan will use this chance to touch Akihisa-kun's chest and buttthat's too sneaky”

“Wh, what are you saying, Mizuki! How can I do such a thing—eh, what? What did you just say? TouchingMizuki, ere you talking about”

“Ah! No, nothing! I' hi the relationshi+p with Akihisa-kun I just said it wrongly!”

“Mizukiere you planning to do to Aki”

In a blink of an eye, I got wrestled down onto the floor by them as they forcefully take away that piece of paper in uysthese techniques aren't moves that amateurs can do!

“Alright, this no6 will be auctioned”

“VERY GOOD, NO MATTER HOW MUCH YOU OFFER, MIHARU WILL BUY IT!”

“““WHY IN THE WORLD IS shi+MIZU-SAN HERE!?”””

“Sorry, but this is a class affair — hm?”

“What's wrong, leader?”

“No, thisisn't 6 It's 9 Yoshi+ just looked at it in the opposite way”

Sugawa-san opens the number in his hand The number 9 has an arrow to indicate how it should be read

“What the hell, so it's 9 That shocked us”

“Yoshi+ really loves to create commotions”

“Causing us to spend so much effort on this”

“It's all Yoshi+'s fault for being unable to see such a simple number like that How stupid”

The FFF ruot 6, I would have been killed

“Well, Aki”

While I' my joints, Minami walks up to me

“Hm? Minami, what's up?”

“What should I say? Wellbefore the s toward and practice a bit? We need to practice on che and rhythm”

Minami starts to warm up as she asked me

Practice for the 2-persons-3-legged race? I see So Mina to make a contribution to the class like that That's nice In contrast, those classmates of mine ould execute me out of jealousy are really rotten until I want them to the mud in their nails

“Ahbut I feel that it's best to train with your own partner, right? It's ether with your partner”

“I' my distance with your body—eh? What did you just say?”

“I just got 9 Didn't you get 6, Minami?”

I open my paper I just drew to Minami for her to see

That's a pity If I could partner with the athletic Minaed race And besides, there would be a lot of happy things happening as well

“Oh, I see So it's like thatif that's the case, it doesn't matter”

Hearing s her shoulders and looks lost as she walks away Did she feel that it would be easier to pair up with ether well If she really thinks this way, it would be really great

“I'h of relief just now”

“Don't worry MizukiI think I would do the sa if our roles were reversed”

Mina It seeirls I shouldn't eavesdrop, and besides, it's tio back to Yuuji and the rest

After keeping the number I opened properly, I turn around to return to my usual friends Yuuji and the rest see about the baseball ot there

“What's wrong, Akihisa? You didn't get the number you want?”

Yuuji ot the nuht? In a certain sense, maybe such an outcome is really the jackpot

Speaking of which, who's my partner?

“Oh ya, Yuuji, what's your number?”

“Huys calot”

“Me too”

“Same here”

It seems like these people haven't decided on their partners in the 2-persons-3-legged race Since the partner number 9 hasn't drawn his number yet, one of these three people will be my partner If that's the case

“Please, Hideyoshi+! You must draw 9!”

“H, Akihisa? You want to be partners with me?”

“Of course! I really want to be partners with Hideyoshi+!”

If it's just Yuuji, Hideyoshi+ and Muttsurini, I would choose Hideyoshi+ without exception Considering the honor of the class, it would be better to choose Yuuji or Muttsurini, but things aren't that sis that are

“We should draw our nues is more important than the baseball tournament as per schedule”

“It will be bad if we don't take part in those events”

“I feel the same”

The 3 of theo, only those 3 haven't drawn numbers yet The only ones with an undecided partner are me, Himeji-san and Minami In other words, once they draw the nuedies of bloodshed

While everyone's trying to hold back their saliva, Hideyoshi+ reaches into the box

Please, Hideyoshi+, get 9!

“Uu, I got 9--”

“BRING IT ON, YOU GUYS!! I'LL DEFEND THIS PIECE OF PAPER EVEN IF I DIE!!!”

“““DON'T THINK THAT YOU CAN LIVE TO SEE THE SUN TOMORROW, IDIOT!!!”””

Not willing to lose to the overwhelhtly There's only a few ins Until then, I must survive!

“--Sorry, sarongly It's 6”

“““”””

The killing intent immediately dissipated At this same time, my enthusiasm disappeared If it's 6, then Hideyoshi+'s partnered with MinamiI feel that it's a pity, but there's a sense of relief here

If that's the case, there's only 7 and 9 left The next one will either be my partner or Himeji-san

“(sssst)”

Muttsurini reaches into the box To hiht? If he can be with Hily self-aware parts That guy will jump into the vortex of happiness even when he knows that he would die I don't want hiet such an envious outcome!

Muttsurini finally pulls out that piece of paper that decides his fate and slowly opens it Noill he get

“9--”

“FAREWELL!!”

“DON'T YOU DARE ESCAPE!! EVERYONE, CATCH SAKAMOTO AND OFFER HIM FOR A BLOOD SACRIFICE!!!”

“OSSSUU!!”