Let n be a positive integer. Let ∑ (-1)k^n(C_k)[(1/2)^k + (3/4)^k + (7/8)^k + (15/16)^k + (31/32)^k]

Question

Let n be a positive integer. Let

\(\displaystyle\sum_{k=0}^{n} (-1)^{k_n}{_C}{_k}\) \(\bigg[\bigg(\frac{1}{2}\bigg)^k + \bigg(\frac{3}{4}\bigg)^k + \bigg(\frac{7}{8}\bigg)^k + \bigg(\frac{15}{16}\bigg)^k + \bigg(\frac{31}{32}\bigg)^k \bigg]\)

If 63A = \(1 - \frac{1}{2^{30}},\) then n is equal to _______.

Answer 1

Answer is (6)