Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.1 Sequences and Series - 14.1 Exercise Set - Page 895: 86

True

$\sum\limits_{k=1}^{n}{c{{a}_{k}}}=c\sum\limits_{k=1}^{n}{{{a}_{k}}}$ $\begin{align} & \sum\limits_{k=1}^{n}{c{{a}_{k}}}=c{{a}_{1}}+c{{a}_{2}}+c{{a}_{3}}+c{{a}_{4}}+\ldots +c{{a}_{n}} \\ & =c\left( {{a}_{1}}+{{a}_{2}}+{{a}_{3}}+{{a}_{4}}+\ldots +{{a}_{n}} \right) \\ & =c\sum\limits_{k=1}^{n}{{{a}_{k}}} \end{align}$ Obtain the left side of the expression, $\sum\limits_{k=1}^{n}{c{{a}_{k}}}=c\sum\limits_{k=1}^{n}{{{a}_{k}}}$ Thus, the statement is true.