Question

Q.Choose the correct answer.
The radius of convergence for power series ∑_(n=1)^∞▒(2^k 〖(x+1)〗^(k+1))/k is
a.3/2
b.1
c.∞
d.½

Answer 1

$$u_k = \frac{2^k}{k}$$

$$R=\lim_{k\to \infin}\frac{u_k}{u_{k+1}}=\lim_{k\to \infin}\frac{2^k}{k}\cdot\frac{k+1}{2^{k+1}}=\frac{1}{2}$$

The correct answer is d) 1/2.