Best luck IIT participants!

Algebra Level 2

Let i = 1 i = \sqrt{-1} . Evaluate

i . i . t = 1 7 t \huge i.i.\sum_{t=1}^7 t


The answer is -28.

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3 solutions

Sudoku Subbu
Apr 10, 2015

consider i × i × t = 1 7 i\times i\times\sum_{t=1}^7 we know that i × i = 1 × 1 = 1 2 = 1 i\times i=\sqrt{-1}\times\sqrt{-1}=\sqrt{-1}^2=-1 and then t = 1 7 = 7 ( 7 + 1 ) 2 = 28 \sum_{t=1}^7=\frac{7(7+1)}{2}=28 therefore the total answer is 1 × 28 = 28 -1\times28=-28

Nihar Mahajan
Mar 28, 2015

i . i . t = 1 7 t i.i.\sum_{t=1}^7 t

= i 2 . ( 7 ) ( 8 ) 2 = i^2 . \dfrac{(7)(8)}{2} (Using the formula of summation).

= ( 1 ) . 56 2 = (-1) . \dfrac{56}{2}

= 28 = -28

@Pranjal Jain @Azhaghu Roopesh M and other students , Best luck for IIT exam!

For IIT? Really?

Aditya Chauhan - 6 years, 2 months ago

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@Aditya Chauhan , This questioin was intended to be easy. P.S. one should never underestimate a question.

Mehul Arora - 6 years, 2 months ago

This a best luck wisher problem , just created for wishing a best luck. This was not for preparation or any revision of IIT test.

Nihar Mahajan - 6 years, 2 months ago

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Exactly. That's true @Aditya Chauhan

Mehul Arora - 6 years, 2 months ago

Thanks ! :D

Keshav Tiwari - 6 years, 2 months ago

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Welcome!! ¨ \ddot\smile

Nihar Mahajan - 6 years, 2 months ago

Now i know why your followers increase exponentially. HEHE

Gautam Sharma - 6 years, 2 months ago

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What you know is what i don't know.Please tell it :)

Nihar Mahajan - 6 years, 2 months ago

Actually it is that you post good level problems but you have posted far more easy level problems than hard ones. So many people are able to do that and hence there is a very high chance that they click the green "Follow " button very often. Seems like a really good logic ,isn't it?

Actually when Azhaghu asked you in one of the notes then it came to my mind but i was not sure,but now i am.

Enjoy.

Gautam Sharma - 6 years, 2 months ago

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The word 'exponentially' surely signifies the presence of @Azhaghu Roopesh M . But I post BOTH tough and easy problems equally .... depends on my mind. I don't think this is the logic .. but there is a true logic which no-one knows (not known to me too).

Nihar Mahajan - 6 years, 2 months ago

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@Nihar Mahajan Or may be the robert downey jr?HEHE

I said that you posted tough questions too but i was saying that some of your questions were very easy like this and have approx 2000 solvers if we say even 3% of people who solved it followed you then it is around 60 followers per easy problem. Pls take it in a light wasy.

I think this is afine logic because only follows you when they come accross you posts and around 2k solvers!!! is a high chance.

Gautam Sharma - 6 years, 2 months ago

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@Gautam Sharma Oh! This may be one reason ... also Robert Downey too :P ...

Nihar Mahajan - 6 years, 2 months ago

@Nihar Mahajan Hmm , how does my presence is being signified here ? I'm at a loss Genius , hep me out ;)

A Former Brilliant Member - 6 years, 2 months ago

Please use a b a \cdot b instead of a . b a.b when denoting multiplication.

Jake Lai - 6 years, 2 months ago

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Sorry about that , but for this problem , '.' is put purposefully used because the expression resembles 'I.I.T' Abbreviation. Thanks!

Nihar Mahajan - 6 years, 2 months ago

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Damn, that's subtle ;) Fine, I shall allow it this once.

Jake Lai - 6 years, 2 months ago

Yeah , nice thinking on your part .

A Former Brilliant Member - 6 years, 2 months ago

Okay!! Will take care!!

Nihar Mahajan - 6 years, 2 months ago

@Azhaghu Roopesh M , THIS PROBLEM , actually I haven't learnt Trigo much yet but still I got it right due to luck! ¨ \ddot\smile

Nihar Mahajan - 6 years, 2 months ago

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Yeah ,you sure are quite lucky :) Just take a look at the number of your followers again and take a look at mine :P

Are you on the B'ant staff ? or are you just playing some kind of trick on me ?

Better start thinking up a 500 followers question !

A Former Brilliant Member - 6 years, 2 months ago

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LoL ... Nothing like that. Yeah 3 more for 500. Which topic do you want for 500 followers problem?? .. xD

Nihar Mahajan - 6 years, 2 months ago

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@Nihar Mahajan Algebra perhaps ? Btw start thinking up a 600 followers question too !

A Former Brilliant Member - 6 years, 2 months ago

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@A Former Brilliant Member Okay! I will think of 600 followers problem too! :) :) . I visited your profile to solve some problems but I saw your 2-3 problems are deleted!

Nihar Mahajan - 6 years, 2 months ago

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@Nihar Mahajan Yeah , I think some mod might have done it by mistake

A Former Brilliant Member - 6 years, 2 months ago
Towhidd Towhidd
Jul 11, 2015

i^2=-1 \sum_{i=1}^7=1+2+3+4+5+6+7 now, -1 (1+2+3+4+5+6+7)=-1 n (n+1)/2=-1 7*8/2=-28

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