Determine whether the given series converges or diverges

Question

Question

Determine whether the given series converges or diverges. Fully justify your answe

(a) $\sum_{n=2}^{\infty} \frac{1}{\sqrt{n} \ln n}$

(b) $\sum_{n=1}^{\infty} \cos \left(\frac{1}{n^{2}}\right)$

(c) $\sum_{n=1}^{x} \frac{(2 n) !}{5^{n} n ! n t}$

math calculus

Answer 1

Answer #1

Summary: we will be using following tests for convergence or divergence of series

Now plotting y=x (red colored) and y=sqrt(x)ln(x) (blue colored) in desmos software.

Nth term test is given by:

(Note that Nth term test just gives information about divergence of a series. We can't conclude anything about convergence of series)

Note: for any query or explanation in any step kindly mention it in the comment section. I will assist you as soon as possible.

Answer 2

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