Detailed Explanations for Calculus 2 Equations

What options do I have for this series? No idea how to do it.
$\sum_{k = 1}^{\infty} \frac{\cos^{2} (k)}{4 k^{2} - 1}$

Yahir Haas 2022-01-21

How to prove:
$\sum_{k = 1}^{\infty} \frac{k - 1}{2 k (1 + k) (1 + 2 k)} = \log_{e} 8 - 2$

Swebaceacichegh 2022-01-21

Suppose $| x | < 1$ . Can you give any ideas on how to find the following sum?
$\frac{x}{x + 1} + \frac{2 x^{2}}{x^{2} + 1} + \frac{4 x^{4}}{x^{4} + 1} + \frac{8 x^{8}}{x^{8}} + 1 + \dots$

Reese Munoz 2022-01-21

Convergence of sequence:
$f (n + 1) = f (n) + \frac{{f (n)}^{2}}{n (n + 1)}$

Sereinserenormg 2022-01-21

How to evaluate the sum:
$S_{n} = \sum_{k = 1}^{n} \frac{k}{k^{4} + \frac{1}{4}}$

jamessinatraaa 2022-01-19

How can I evaluate
$\sum_{n = 1}^{\infty} \frac{2 n}{3^{n + 1}}$

Joan Thompson 2022-01-19

How can we prove that?
$\sum_{n = 1}^{\infty} \frac{x^{3 n}}{(3 n - 1)!} = \frac{1}{3} e^{\frac{- x}{2}} x (e^{\frac{3 x}{2}} - 2 \sin (\frac{π + 3 \sqrt{3} x}{6}))$

Mary Hammonds 2022-01-19

How do I prove:
$lim_{n \to + \infty} \sqrt[n]{n!}$ is infinte?

Chris Cruz 2022-01-19

How to find infinite sum How to find infinite sum
$1 + \frac{1}{3} + \frac{1 \cdot 3}{3 \cdot 6} + \frac{1 \cdot 4 \cdot 5}{3 \cdot 6 \cdot 9} + \frac{1 \cdot 3 \cdot 5 \cdot 7}{3 \cdot 6 \cdot 9 \cdot 12} + \dots$

Sandra Allison 2022-01-18

Can you please explain why
$\sum_{k = 1}^{\infty} \frac{k}{2^{k}} = 2$

Sandra Allison 2022-01-18

Test the condition for convergence of
$\sum_{n = 1}^{\infty} \frac{1}{n (n + 1) (n + 2)}$
and find the sum if it exists.

Joanna Benson 2022-01-18

How to show the following equality?
$\sum_{n = 0}^{\infty} \frac{1}{a^{2} + n^{2}} = \frac{1 + a π \coth a π}{2 a^{2}}$

Daniell Phillips 2022-01-18

Find the sum:
$S = \sum_{k = 1}^{\infty} \frac{1}{k^{2} - a^{2}}$
where $a \in (0, 1)$

Madeline Lott 2022-01-17

How to prove:
$\sum_{n = 0}^{\infty} \frac{n^{2}}{2^{n}} = 6$

Roger Smith 2022-01-17

Calculate: $\lim_{n \to \infty} e^{- n} \sum_{k = 0}^{n} \frac{n^{k}}{k!}$

Shirley Thompson 2022-01-16

Showing that:
$lim_{n \to \infty} \frac{\sqrt[n]{n!}}{n} = \frac{1}{e}$

eliaskidszs 2022-01-16

I encountered while learning about definite integrals:
$\sum_{k = 1}^{n} k^{2} = \frac{n (n + 1) (2 n + 1)}{6}$

Joyce Smith 2022-01-07

Evaluate the indefinite integral.
$\int \frac{\cos \sqrt{t}}{\sqrt{t}}$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2