Question

$sum_{n=1}^{infty} frac{sqrt{n}}{n^2 + 2n - 1}$ ewline $sum_{n=1}^{infty} frac{(-1)^{n-1}}{n^{1/3}}$ ewline $sum_{n=1}^{infty} (-1)^{n-1} n^{1/3}$ ewline $sum_{n=2}^{infty} frac{cos npi}{(ln n)^2}$

          $sum_{n=1}^{infty} frac{sqrt{n}}{n^2 + 2n - 1}$ 
ewline $sum_{n=1}^{infty} frac{(-1)^{n-1}}{n^{1/3}}$ 
ewline $sum_{n=1}^{infty} (-1)^{n-1} n^{1/3}$ 
ewline $sum_{n=2}^{infty} frac{cos npi}{(ln n)^2}$

$sumn=1^infty fracsqrtnn^2 + 2n - 1 ewline sumn=1^infty frac(-1)^n-1n^1/3 ewline sumn=1^infty (-1)^n-1 n^1/3 ewline sumn=2^infty fraccos npi(ln n)^2$

Added by Nicholas B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

09/18/2023

Step 1

Vn = 8 / (n^2 + 2n - 1), n = 1 To determine whether this series converges or diverges, we can use the limit comparison test. We compare it to the series 1/n^2, which is a known convergent series. Taking the limit as n approaches infinity, we have: lim (n->∞) (8 / Show more…

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