11yes its one of the values bring out the general expression
7 Answers
621) it has to be of the form 4k-1
what else?
When it is of the form 8k - 1 , we are sure that the sum is zero.
now then it is of the form 8k-5, then the real issue is...
The sum to me "seems not zero.. for any of those numbers" but that is more instinct based.
so to me the answer should be
8k-1!
11should i post the solution
or a hint
hint is think of binomial expansion
62(1+ix)^m
and
(1-ix)^m
then you will get
mCr xr. ir
and
mCr xr. ir (-1)r
We take their sum and difference! and then their difference!!
I hope tihs is something useful and not a stupid invention of my mind! cos right now i am half awake.
11i dont think we need (1+ix)we dont need x here
expansion of the series (1+i)mis the ques and cmparin real and imaginaary parts we get the ans