## Calculus 8th Edition

If $\sum c_{n}6^{n}$ is convergent then $\lim\limits_{n \to \infty}c_{n}6^{n}=0$ For limit to be zero, $c_{n}$ must be less than $\frac{1}{6^{n}}$ For $\sum c_{n}(-2)^{n}$, since it is an alternating series then $\lim\limits_{n \to \infty}c_{n}(-2)^{n}=0$.Since, we know that $c_{n}\lt\frac{1}{6^{n}}$ thus, $c_{n}\lt\frac{1}{(-2)^{n}}$ and limit does go to zero . Therefore, $\sum c_{n}(-2)^{n}$ is convergent by the Alternating Series Test. Hence, the statement is true.