P.T:
(n c 0) (2n c n) - (n c 1) (2n-1 c n) +....
[(-1)^n] (n c n) (n c n)] =8
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1 Answers
1u got the question rong .......
we have to prove if L.H.S. = 1 not 8
2nCn is coefficient of xn in expansion of (1+x)2n
2n-1Cn is coefficient of xn in expansion of (1+x)2n-1
2n-2Cn is coefficient of xn in expansion of (1+x)2n-2
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nCn is coefficient of xn in expansion of (1+x)n
we have L.H.S = C0.2nCn-C12n-1Cn- ........ (-1)n CnnCn
= coefficient of xn in [C0(1+x)2n - C1(1+x)2n-1 + ....+(-1)nCn(1+x)n
= coefficient of xn in(1+x)n [C0(1+x)n - C1(1+x)n-1 + ....+(-1)nCn]
= coefficient of xn in(1+x)n [(1+x)-1]n
= coefficient of xn in(1+x)n xn
= 1
= R.H.S
