Calculus Examples of Geometric Series and More

Sum of the series:
$\sum_{n = 0}^{\infty} \frac{1 + n}{3^{n}}$

iristh3virusoo2 2022-02-24

How can I calculate
$\sum_{n = 1}^{n = 1} \frac{{(- 1)}^{n}}{16 n^{2} - 1}$
using the Fourier series?

sweetrainyday8s2 2022-02-24

Does the series
$\sum_{n = 1}^{\infty} \sin (2 π \sqrt{n^{2} + a^{2} \sin n + {(- 1)}^{n}})$
converge?

Cian Orr 2022-02-24

I want to evaluate the sum
$\sum_{n = 2}^{\infty} \frac{n^{4} + 3 n^{2} + 10 n + 10}{2^{n} (n^{4} + 4)}$

trasbocohf1 2022-02-24

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

Myah Fuller 2022-02-24

Identify
$f (x) = \sum_{k = - \infty}^{\infty} \frac{1}{{(x + k)}^{2}}$

lovesickgirlsrd5 2022-02-24

Prove that
$\sum_{n = 0}^{\infty} \frac{(2 n + 1)!}{2^{3 n} {(n!)}^{2}}$
converges to $2 \sqrt{2}$

Cobie Sadler 2022-02-24

Proving:
$\sum_{n = 0}^{\infty} \frac{\sin^{4} (4 n + 2)}{{(2 n + 1)}^{2}} = \frac{5 π^{2}}{16} - \frac{3 π}{4}$

dristauwaz 2022-02-24

How to prove:
$\sum_{n = 1}^{\infty} \frac{1}{16 n^{2} - 16 n + 3} = \frac{π}{8}$

Kris Patton 2022-02-24

Please help me, to prove that
$\sum_{n = 2}^{\infty} \frac{2}{(n^{3} - n) 3^{n}} = - \frac{1}{2} + \frac{4}{3} \sum_{n = 1}^{\infty} \frac{1}{n \cdot 3^{n}}$

haciendodedorcp 2022-02-24

Prove:
$\cos (\frac{2 π}{5}) + \cos (\frac{4 π}{5}) + \cos (\frac{6 π}{5}) + \cos (\frac{8 π}{5}) = - 1$

Zeenat Horn 2022-02-24

Prove $\sum_{k = 1}^{\infty} \frac{{(- 1)}^{k}}{k} \sum_{j = 1}^{2 k} \frac{{(- 1)}^{j}}{j} = \frac{π^{2}}{48} + \frac{1}{4} \ln^{2} 2$

klancimarsn 2022-02-24

How to show that
$\sum_{n = 1}^{\infty} \frac{1}{n^{2} + 3 n + 1} = \frac{π \sqrt{5}}{5} \tan \frac{π \sqrt{5}}{2}$

Tagiuraoob 2022-02-24

Evaluate
$\sum_{n = 1}^{\infty} \frac{ϕ (n)}{7^{n} + 1}$

Keri Molloy 2022-02-24

How to get the sum of the series
$\sum_{n = 1}^{\infty} \frac{1}{{(4 n^{2} - 1)}^{2}}$ ?

cindakayumn 2022-02-24

Prove that:
$lim_{m \to \infty} \sum_{k = 1}^{m} \frac{2^{- k}}{k} = \log 2$

geekotakuglh 2022-02-24

Evaluate the series:
$\sum_{k = 1}^{\infty} \frac{1}{k {(k + 1)}^{2} k!}$

Ingrid Senior 2022-02-24

How to prove:
$\sum_{n = 1}^{\infty} (\frac{1}{4 n + 1} - \frac{1}{4 n}) = \frac{1}{8} (π - 8 + 6 \ln 2)$

Beverley Rahman 2022-02-23

Can we find a sequence $a_{n}$ such that $lim_{n \to \infty} a_{n} = \infty$ , but
$lim_{n \to \infty} \frac{1}{n} \sum_{i = 1}^{n} a_{i} = a < \infty$ ?

Carole Juarez 2022-02-23

Show whether the series converges.
$\sum_{n = 1}^{\infty} \int_{0}^{\frac{1}{\sqrt{n}}} \frac{e^{x} - 1}{1 + x} d x$

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