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Sergio [31]
3 years ago
11

Does this sum converge: show steps

Mathematics
1 answer:
ehidna [41]3 years ago
6 0

Answer:

Yes

Step-by-step explanation:

\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }

If we say u = √n, then:

\sum_{u=1}^{\infty} (\frac{1}{e})^{u}

This is a geometric series.  Since |1/e| < 1, the series converges.

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