Konverge I

Calculus Level 3

$\large \begin{aligned} A & = \sum_{n=1}^{\infty} \dfrac{(-1)^n \cdot n}{\sqrt{n^3+4}} \\ B & = \sum_{n=1}^{\infty} \dfrac{(2n)!}{(n!)^2} \\ C & = \sum_{n=0}^{\infty} \dfrac{1 + \sin(n^e)}{e^n} \end{aligned}$

Which of the series above are convergent?

A

B

and

C

A

and

C

None of them Only

A

Only

C

B

and

C

A

and

B

Only

B

1 solution

Guilherme Dela Corte
Sep 26, 2017

Hints: $A$ is decreasing, alternate and $\lim_{n \to \infty} \dfrac{n}{\sqrt{n^3+4}} = 0$ .

$B$ is increasing.

$C < \displaystyle \sum \frac{2}{e^n}$ .

Konverge I

1 solution

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