If $\sum_{n=1}^{\infty} a_{n}$ converges then $\sum_{n=1}^{\infty} k a_{n}$ converges (k $\neq$ 0).

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Quizplus · Accepted Answer

If $\sum_{n=1}^{\infty} a_{n}$ converges, then multiplying each term by a constant $k$ (where $k \neq 0$) simply scales the series by $k$, and the resulting series $\sum_{n=1}^{\infty} k a_{n}$ also converges. This is because the convergence of a series is determined by the behavior of its terms as $n$ approaches infinity, and scaling does not affect whether the series sum approaches a finite limit.

If ∑n=1∞an\sum_{n=1}^{\infty} a_{n}∑n=1∞​an​ Converges Then ∑n=1∞kan\sum_{n=1}^{\infty} k a_{n}∑n=1∞​kan​ Converges (K ≠\neq= 0)

If $\sum_{n=1}^{\infty} a_{n}$ Converges Then $\sum_{n=1}^{\infty} k a_{n}$ Converges (K $\neq$ 0)