Calculus Examples of Geometric Series and More

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
$lim_{n \to \infty} {(1 - \frac{a_{n}}{n})}^{n}$

iocasq4 2022-01-24

How to prove the following sequence converges to 0.5?
$a_{n} = \int_{0}^{1} \frac{n x^{n - 1}}{1 + x} d x$

2alr8w 2022-01-24

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

Alisha Pitts 2022-01-24

Compute
$lim_{n \to \infty} \sum_{k = 1}^{n} \arcsin (\frac{k}{n^{2}})$

Jazmin Perry 2022-01-24

I need to find the limit of the following sequence:
$lim_{n \to \infty} \prod_{k = 1}^{n} (1 + \frac{k}{n^{2}})$

minikim38 2022-01-24

Find the value of
$1 {\sin 2}^{\circ} + 2 {\sin 4}^{\circ} + 3 {\sin 6}^{\circ} + \dots + 90 {\sin 180}^{\circ}$

Vanessa Hensley 2022-01-23

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

GrareeCowui 2022-01-23

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

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 $lim_{n \to \infty} a_{n} = \infty$

The majority of questions about series calculus that you will find online will have odd solutions that do not really provide explanations or the answers that would help one understand how things work. We have taken a different approach by offering series calculus practice questions that are connected with initial equations that must be solved. It is once again about estimation and analysis as the examples include the building of the bridges and calculation of the power or energy necessary to implement the safest solution by estimating the best one. By offering clear examples, we help you learn things easier!

Calculus 2

Calculus Series: Understanding Geometric Examples