Question

Determine whether the series $\sum_{n=0}^{\infty} e^{-\frac{9n}{2}}$ converges or diverges. If it converges, find its sum.

Name: Determine whether the series ∑n=0^∞ e^-(9n)/(2) converges or diverges. If it converges, find its sum.
Uploaded: 2023-05-05T18:49:11-08:00
Duration: 59 s
Channel: Sam Stansfield
Description: Determine whether the series ∑n=0^∞ e^-(9n)/(2) converges or diverges. If it converges, find its sum.

          Determine whether the series $\sum_{n=0}^{\infty} e^{-\frac{9n}{2}}$ converges or diverges. If it converges, find its sum.

Added by Jeff S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

05/05/2023

Step 1

The ratio test states that for a series \sum a_n, if lim_(n->\infty) |a_(n+1)/a_n| < 1, then the series converges. If lim_(n->\infty) |a_(n+1)/a_n| > 1 or does not exist, then the series diverges. In this case, a_n = e^(9n/2). Let's calculate the ratio Show more…

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