Determine whether the series converges or diverges. [ sum_{n=1}^{infty} frac{sqrt{1+n}}{8+n} ] converges diverges

          Determine whether the series converges or diverges.
[
sum_{n=1}^{infty} frac{sqrt{1+n}}{8+n}
]
converges
diverges

$Determine whether the series converges or diverges. [ sumn=1^infty fracsqrt1+n8+n ] converges diverges$

Added by Fhyyd F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ivan Kochetkov

05/05/2023

Step 1

We will compare our given series to another series that we know converges or diverges. Consider the series \[ \sum_{n=1}^{\infty} \frac{\sqrt{n}}{n} \] We can rewrite this series as \[ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} \] Now, we know that the series \[ Show more…

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