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Show that the sum of the coefficients of the odd terms in the expansion of (1+x) 2n is 2 2n-1 .

Show that the sum of the coefficients of the odd terms in the expansion of (1+x)2n is 22n-1.

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
As we know
 
in (1+x )^n 
c0 + c1 +c2 + c3 +c4+ c5+c6 +........ = 2^n
 
and
c1 + c3 + c5 + c7 + …... = 2^n-1
 
similarly
in (1+x)^2n 
 
c1 + c3 + c5 + …... = 2^(2n -1)

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