O4440 O4440
  • 01-12-2019
  • Mathematics
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does this sum converge: show steps

does this sum converge show steps class=

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MathPhys
MathPhys MathPhys
  • 01-12-2019

Answer:

Yes

Step-by-step explanation:

[tex]\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }[/tex]

If we say u = √n, then:

[tex]\sum_{u=1}^{\infty} (\frac{1}{e})^{u}[/tex]

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

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