Question

Determine the radius of convergence of the following power series.

Σ(-1)^k x^k/3^k

Answer 1

(−1)kxk

Explanation:

Therefore, the infinite series ∞∑k=11k does not converge.

(−1)kxk = 1 − x + x2 − x3 + ···. = ∞. ∑ k=0. (−x)k = 1. 1 − (−x). = 1. 1 + x ... 3. )k. = x. 1 − (x2/3). = 3x. 3 − x2 for |x2/3| < 1. 1.2 Radius of Convergence.