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

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

Grade:11

3 Answers

Shyama P
35 Points
9 years ago

ans : 249

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

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

you get: 50C0+50C1+.........+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+....

nikhil arora
54 Points
9 years ago

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

so answer shud be 250-1 = 249

Ranjita yadav
35 Points
9 years ago

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

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