If $\sum C_{n} 6^{n}$ is convergent, then $\sum C_{n}(-6)^{n}$ is also convergent.

Name: If $\sum C_{n} 6^{n}$ is convergent, then $\sum C_{n}(-6)^{n}$ is also convergent.
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Question

Quizplus · Accepted Answer

The convergence of $\sum C_{n} 6^{n}$ does not guarantee the convergence of $\sum C_{n}(-6)^{n}$ because the alternating signs in the latter series can affect its convergence properties differently than the series with all positive terms.

If ∑Cn6n\sum C_{n} 6^{n}∑Cn​6n Is Convergent, Then ∑Cn(−6)n\sum C_{n}(-6)^{n}∑Cn​(−6)n Is Also Convergent

If $\sum C_{n} 6^{n}$ Is Convergent, Then $\sum C_{n}(-6)^{n}$ Is Also Convergent