The 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.
Related questions
In the expansion of a bracket raised to four, the sum of indices is:How many terms are in the expansion of a bracket raised to twelve?How many terms are in the expansion of a bracket raised to five?In the last term of the expansion, the index of b is:In the first term of the expansion, the index of b is:In the first term of the expansion, the index of a is:The general rule for expansion is built using the concept of:Why is Pascal's triangle awkward for a large index?