Detailed Explanations for Calculus 2 Equations

Find the sum of series:
$\sum_{n = 0}^{\infty} \frac{(4 n)!}{(4 n + 4)!}$

iristh3virusoo2 2022-02-23

I would like to find the exact value of the series
$\sum_{n = 3}^{\infty} \frac{4 n - 3}{n (n^{2} - 4)}$

lovesickgirlsrd5 2022-02-23

Consider the series
$\sum_{n = 1}^{\infty} (e^{- n^{2}} - e^{- {(n + x)}^{2}}$

fecundavai3c 2022-02-23

Does this double series has closed form (i.e. can be computed) ?
$\sum_{m = 1}^{\infty} \sum_{n = 1}^{\infty} \frac{1}{10^{n m}}$

Scoopedepalj 2022-02-23

How to prove
$\sum_{n = 1}^{\infty} \arctan \frac{10 n}{(3 n^{2} + 2) (9 n^{2} - 1)} = \ln 3 - \frac{π}{4}$

Nyah Conrad 2022-02-23

$\sum_{n = 1}^{\infty} \frac{{(\sin n + 2)}^{n}}{n 3^{n}}$
Does it converge or diverge?

sunyerneq 2022-02-23

Proving that:
$\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n + 1}}{n^{2}} = \frac{π^{2}}{12}$

embeucadaoo8 2022-02-23

I want to show that
$\sum_{k = 1}^{n - 1} \frac{1}{1 - \cos (\frac{2 k π}{n})} = \frac{n^{2} - 1}{6}$

Layla-Rose Ellison 2022-02-22

Author introduces an alternating series:
$\sum_{n = 1}^{\infty} {(- 1)}^{n} \frac{(2 n)!}{4^{n} {(n!)}^{2}}$

demonlikw4 2022-02-22

I was able to prove this sum
$\sum_{n = 1}^{\infty} \frac{1}{n + 3^{n}}$

Sarah-Louise Prince 2022-02-22

Compute the limit:
$\sum_{k = 1}^{\infty} \ln (1 + \frac{1}{4 k^{2}})$

Zaynah Dunn 2022-02-22

How would you tackle this series by real analysis?
$\sum_{n = 1}^{\infty} \sum_{m = 1}^{\infty} \frac{1}{m^{4} (m^{2} + n^{2})}$

cooopt392a0i 2022-02-22

Proof:
$\sum_{n = 0}^{\infty} \frac{n^{2} + 3 n + 2}{4^{n}} = \frac{128}{27}$
Given hint: $(n^{2} + 3 n + 2) = (n + 2) (n + 1)$

Carole Juarez 2022-02-22

How do we find
$S = \sum_{k = 1}^{\infty} [\frac{1}{2 k} - \log (1 + \frac{1}{2 k})]$

trasbocohf1 2022-02-22

Is there a closed-form of
$\sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{(2 n + 1) (2 n + 2) (2 n + 3) (2 n + 4)}$

cindakayumn 2022-02-22

How to read and execute this sum?
$\sum_{1 \leq l < m < n} \frac{1}{5^{l} 3^{m} 2^{n}}$

tumahimikgjr 2022-02-22

When does this series:
$\sum_{n = 0}^{\infty} \sin (n! π x)$
converge?

Akbar Witt 2022-02-22

Find:
$\sum_{k = 1}^{\infty} \frac{1}{k (k + 1) (k + 2) (k + 3)}$

Keri Molloy 2022-02-22

Prove the converges of
$\sum_{n = 1}^{\infty} \frac{\sqrt{2 n - 1} \ln (4 n + 1)}{n (n + 1)}$

sunyerneq 2022-02-22

Find:
$\sum_{k = 1}^{\infty} \frac{6^{k}}{(3^{k + 1} - 2^{k + 1}) (3^{k} - 2^{k})}$

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

Calculus 2 Equations: Expert Solutions and More