If ∑ n = 0 ∞ c n x n {\displaystyle \sum _{n=0}^{\infty }c_{n}x^{n}} converges, does it follow that the following series converges?
(a) ∑ n = 0 ∞ c n ( x 2 ) n {\displaystyle \sum _{n=0}^{\infty }c_{n}{\bigg (}{\frac {x}{2}}{\bigg )}^{n}}
(b) ∑ n = 0 ∞ c n ( − x ) n {\displaystyle \sum _{n=0}^{\infty }c_{n}(-x)^{n}}
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