Series Convergence

Question

Find all the values of x such that the given series would converge.

∑n=1 to ∞ [2^n(x−4)^n(n+1)]/(n+10)

Give your answer in interval notation.

Answer 1

Use the ratio test to find Lim 2(x-4)²(N+10)/(N+11) as N → ∞ = 2(x-4)². Note that 2(x-4)²<1 to converge requiring -.707<x<+.707