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Ice Inkberry
Ice Inkberry
13:37
Sometimes I forget simplest of stuff. Someone please remind me how we do this?
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Abcd
Abcd
14:08
See:
$(1+x)^n = 1 + nx + n(n-1)/2! x^2 + n(n-1)(n-2)/3! x^3...$
$(1-x)^{-n} = 1+ nx + \dfrac{n(n+1)}{2!}x^2 + \dfrac{n(n+1)(n+2)x^3}{3!}+...$
$(1-x)^{-n} = 1 + {^n}C_1 x+ {^{n +1}}C_2x^2 +... $
@IceInkberry I think there's a mistake in what you have written
$(1-x^6)^3 \ne (1- 3x^6)$
Jasmine
Jasmine
@Abcd not in portion
Abcd
Abcd
Then, the series of $(1-x)^{-3}$ I have written above^
← 3 messages moved from JEE/High School Chemistry Problems
@IceInkberry OK?
@Jasmine hmm,
Ice Inkberry
Ice Inkberry
@Abcd I have written what was written in the solution
Jasmine
Jasmine
@IceInkberry that's just to take out the coefficients of $x^8 $ rest are not required
Abcd
Abcd
@IceInkberry Are you happy with the series of $(1-x)^{-n}$ that I have sent above?
$(1-x^6 )^3$ = $(1-x^{18} -3x^6(1-x^6) )$
@IceInkberry Now they have purposely removed higher powers
because keeping them doesnt change the answer
@IceInkberry Now happy!?
Ice Inkberry
Ice Inkberry
14:19
@Abcd I am happy. I actually knew it. But, I don't know how they did that
Oh okay, will see how they did for 8th power.

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