Solve the problem.
-$\text { If } \sum a _ { n } \text { is a convergent series of nonnegative terms, what can be said about } \sum a _ { n } k \text {, where k is a positive integer? }$
A) Always diverges
B) Always converges
C) May converge or diverge

Question

Quizplus · Accepted Answer

Since $\sum a_n$ is a convergent series of nonnegative terms, multiplying each term by a positive integer $k$ simply scales the series by a constant factor. The series $\sum a_n k$ remains convergent because scaling a convergent series by a constant factor does not affect its convergence.

Solve the Problem A) Always Diverges B) Always Converges C) May Converge or _

Solve the Problem A) Always Diverges
B) Always Converges
C) May Converge or _