Calculus Examples of Geometric Series and More

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

London Douglas 2022-04-02

Sums of logarithms:
$\sum_{k = a + 1}^{b} \log (1 + \frac{1}{k})$

Jackson Floyd 2022-04-02

Summing up the series $a_{3} k$ where
$\log (1 - x + x^{2}) = \sum a_{k} x^{k}$

Pablo Dennis 2022-04-02

Summation of a non trivial series
$\sum_{m = 2}^{10^{6}} \sum_{n = 1}^{\infty} \frac{m^{n} + m^{- n}}{m^{n}}$
where $n = integer nearest to the \sqrt{n}$

nastupnat0hh 2022-04-02

Sum of series:
$\arctan (n + 1) - \arctan (n + 2)$ where n varies from 0 to infinity.

Oxinailelpels3t14 2022-04-01

I have to solve this recurrence using substitutions:
$(n + 1) (n - 2) a_{n} = n (n^{2} - n - 1) a_{n - 1} - {(n - 1)}^{3} a_{n - 2}$ with $a_{2} = a_{3} = 1$

loraliyeruxi 2022-04-01

I am trying to find the common ratio of $\sum_{n = 0}^{\infty} 2^{- n} z^{n^{2}}$

Taylor series of $\frac{x^{2}}{2} - 1 + \cos x$ using power series operations

Jaylin Clements 2022-03-31

Solving summation problem
$\sum_{i = x}^{2 x} 5 - \sum_{k = 2 x + 1}^{5 x + 2} 5 = - 25$

calcolare45pj 2022-03-30

Proved that question:
$S (n) = \sum_{k \geq 1} \frac{n!}{k (n - k)! n^{k}} = \sum_{k \geq 1} \frac{n^{\underset{―}{k}}}{k n^{k}} \approx \frac{1}{2} \log (n)$

abitinomaq1 2022-03-29

Proving identity
$\sum [{(j + t)}^{- 1} - j^{- 1}] = \sum_{k \geq 1} ζ (k + 1) {(- t)}^{k}$

xxgetthisar08 2022-03-28

Determining convergence of a series
$\sum_{n = 0}^{\infty} \sqrt{n} (\sqrt{n^{4} + 1} - n^{2})$

xxgetthisar08 2022-03-28

Convergence of a series and respective sum:
$\sum_{n \geq 0} {(\frac{2}{3})}^{2 n - 1}$

tibukooinm 2022-03-27

Computing the sum of the ratios:
$S_{n} = \sum_{k = 0}^{n} \frac{n - k + 1}{(n + 1) (n + 2) (n - k + 2)}$

calcolare45pj 2022-03-27

Help calculating a series
$\sum_{n = 0}^{4} 2 n$

Jaylin Clements 2022-03-26

Given the following series: $\sum_{n = 1}^{\infty} {(\sqrt[3]{n + 1} - \sqrt[3]{n - 1})}^{α}$ where $α \in R$ . Does the series converge or diverge?

Lorelei Stanton 2022-03-25

How do I calculate the sum of this series?
$\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n 2^{n + 1}}$

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