Asked by Anonymous
Determine whether the series is convergent or divergent.∑from k=1to ∞ (ke^-9k)
Answers
Answered by
oobleck
since e^(-9k) goes to zero much faster than k grows, the series converges.
Use the ratio test.
A_(n+1)/A_n = (k+1)e^(-9k-9)/ke^(-9k)
= (k+1)/k * e^-9
Use the ratio test.
A_(n+1)/A_n = (k+1)e^(-9k-9)/ke^(-9k)
= (k+1)/k * e^-9
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