If $\sum _ { n = 1 } ^ { \infty } c _ { n } ( x - n ) ^ { n }$ is convergent at $x = 5$ , what can be said about the convergence or divergence of the following series?
(a) $\sum _ { n = 1 } ^ { \infty } c _ { n }$ (b) $\sum _ { n = 1 } ^ { \infty } c _ { n } ( - 2 ) ^ { n }$ (c) $\sum _ { n = 1 } ^ { \infty } c _ { n } 4 ^ { n }$

Question

Quizplus · Accepted Answer

The Answer of If $\sum _ { n = 1 } ^ { \infty } c _ { n } ( x - n ) ^ { n }$ is convergent at $x = 5$ , what can be said about the convergence or divergence of the following series?
(a) $\sum _ { n = 1 } ^ { \infty } c _ { n }$ (b) $\sum _ { n = 1 } ^ { \infty } c _ { n } ( - 2 ) ^ { n }$ (c) $\sum _ { n = 1 } ^ { \infty } c _ { n } 4 ^ { n }$

If ∑n=1∞cn(x−n)n\sum _ { n = 1 } ^ { \infty } c _ { n } ( x - n ) ^ { n }∑n=1∞​cn​(x−n)n

If $\sum _ { n = 1 } ^ { \infty } c _ { n } ( x - n ) ^ { n }$