alleryThe sum of coefficients of ODD powers of x in (1 + x)^10 equals
A2^9 = 512
B2^10 = 1024
C2^5 = 32
D2^8 = 256
Answer & Solution
Correct answer: A. 2^9 = 512
(1 + x)^n + (1 − x)^n has only even-power coefficients doubled.
At x = 1 sum of all = 2^n, sum of even-power = (2^n + 0)/2 ?...
**Cleaner:** odd-power coefficients sum to ((1+1)^n − (1−1)^n)/2 = 2^n / 2 = 2^(n−1) = 2^9 = 512.
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