Detailed Explanations for Calculus 2 Equations

Determine convergence of the series
$\sum_{n = 1}^{\infty} \frac{(2 n - 1)!!}{(2 n)!!}$

Emerson Barnes 2022-01-24

I try to solve the following sum:
$\sum_{k = 1}^{\infty} \sum_{n = 1}^{\infty} \frac{1}{k^{2} n + 2 n k + n^{2} k}$

Emerson Barnes 2022-01-24

What is the value of
$\sum_{k = 1}^{\infty} \frac{1}{(3 k + 1) (3 k + 2)}$

Autohelmvt 2022-01-24

Prove that:
$\sum_{n = 1}^{\infty} \frac{n^{2} (n - 1)}{2^{n}} = 20$

Anika Osborne 2022-01-24

If $a_{n} = {(1 + \frac{2}{n})}^{n}$ , then find
$lim_{n \to \infty} {(1 - \frac{a_{n}}{n})}^{n}$

2alr8w 2022-01-24

I need to find:
$lim_{n \to \infty} n \sum_{k = n}^{\infty} \frac{1}{2 k (2 k + 1)}$

ardeinduie 2022-01-23

What tools would you gladly recommend me for computing precisely the limit below? Maybe a starting point?
$lim_{n \to \infty} \frac{1}{\log (n)} \sum_{k = 1}^{n} \frac{\cos (\sin (2 π \log (k)))}{k}$

Marquis Neal 2022-01-23

How to prove that
$\sum_{k \geq 1} \frac{1}{2^{k} k^{2}} = \frac{π^{2}}{12} - \frac{1}{2} {\log (2)}^{2}$

William Montgomery 2022-01-23

I want to try and evaluate this interesting sum:
$\sum_{n = 1}^{\infty} \frac{1}{Γ (n + s)}$
where $0 \leq s < q$

Jaeden Frederick 2022-01-23

How to show that that $\sum_{n = 1}^{\infty} (\frac{1}{3 n - 1} + \frac{1}{3 n - 2} - \frac{2}{3 n}) = \ln (3)$

GrareeCowui 2022-01-23

Proof that:
$\sum_{n = 0}^{\infty} \frac{1}{n!} = e$

Vanessa Hensley 2022-01-23

Find
$lim_{n \to \infty} \frac{{(n + 1)}^{\sqrt{n + 1}}}{n^{\sqrt{n}}}$

poveli1e 2022-01-23

Evaluate the limit
$lim_{n \to \infty} {(\frac{n + 1}{n})}^{n^{2}} \cdot \frac{1}{e^{n}}$

ndimiimpercea2 2022-01-23

Evaluate
$lim_{x \to \infty} {(\sum_{n = 1}^{\infty} {(\frac{x}{n})}^{n})}^{\frac{1}{x}}$

Gerald Ritter 2022-01-23

So i have the following sequence:
$1, 1, 2, 2, 2, 3, 4, 5, 5, 4, 4, 4, 4, 4, 5, \dots$
I would like to know the n-th term of this sequence.

derlingasmh 2022-01-23

I am confused on the following series:
$\sum_{n = 1} \frac{1}{n (n + 1)} = 1$

Rylan Duncan 2022-01-23

Sum of series:
$\sum_{n = 1}^{\infty} \frac{1}{4 n^{2} - 1}$

Alex Cervantes 2022-01-23

Show that $A_{n} = \sum_{k = 1}^{n} \sin k$ is bounded?

poveli1e 2022-01-23

Evaluate $\sum_{n = 1}^{\infty} \frac{1}{n^{4}}$ using Parseval's theorem (Fourier series).

iocasq4 2022-01-23

Prove that:
$lim_{n \to \infty} {(1 + \frac{1}{a_{n}})}^{a_{n}} = e$ if $lim_{n \to \infty} a_{n} = \infty$

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