In the expansion of (1+x)50 , the sum of the coefficients of odd powers of x is??

ans : 2⁴⁹

(1+x)⁵⁰ = 1+⁵⁰C₁ x+⁵⁰C₂ x² +........+⁵⁰C₅₀ x⁵⁰ 

Put x=1 & x=-1 in the expansion.

you get: ⁵⁰C₀₊⁵⁰C_1+.........+⁵⁰C₅₀₌₂⁵⁰ & ⁵⁰C0+⁵⁰C₂+.....+⁵⁰C₅₀=⁵⁰C1+......+⁵⁰C₄₉

Req. sum =⁵⁰C1+......+⁵⁰C₄₉₌₂⁵⁰/2=2⁴⁹

thats the derivation of the formulas:

nC0+nC1+....+nCn=2ⁿ   and

nC0+nC2+....=nC1+nC3+....

nC1 + nC2 + nC3 ...... = 2^n-1

so answer shud be 2^50-1 = 2⁴⁹

Approved

why u put x=1 & -1...??