Calculus Examples of Geometric Series and More

What options do I have for this series? No idea how to do it.
$\sum_{k = 1}^{\infty} \frac{\cos^{2} (k)}{4 k^{2} - 1}$

Yahir Haas 2022-01-21

How to prove:
$\sum_{k = 1}^{\infty} \frac{k - 1}{2 k (1 + k) (1 + 2 k)} = \log_{e} 8 - 2$

Swebaceacichegh 2022-01-21

Suppose $| x | < 1$ . Can you give any ideas on how to find the following sum?
$\frac{x}{x + 1} + \frac{2 x^{2}}{x^{2} + 1} + \frac{4 x^{4}}{x^{4} + 1} + \frac{8 x^{8}}{x^{8}} + 1 + \dots$

Reese Munoz 2022-01-21

Convergence of sequence:
$f (n + 1) = f (n) + \frac{{f (n)}^{2}}{n (n + 1)}$

Sereinserenormg 2022-01-21

How to evaluate the sum:
$S_{n} = \sum_{k = 1}^{n} \frac{k}{k^{4} + \frac{1}{4}}$

absolutestylehc 2022-01-21

Given
$1 \cdot 2^{1} + 2 \cdot 2^{2} + 3 \cdot 2^{3} + 4 \cdot 2^{4} + \dots + d \cdot 2^{d} = \sum_{r = 1}^{d} r \cdot 2^{r}$
how can we infer to the following solution?
$2 (d - 1) \cdot 2^{d} + 2$

stropa0u 2022-01-21

Prove the following inequality for every $n \geq 1$ :
$\sum_{k = 1}^{n} \frac{1}{k^{2} + 3 k + 1} \leq \frac{13}{20}$

kuntungw3 2022-01-21

Find $\sum_{n = 0}^{\infty} \frac{2^{n}}{3^{2^{n} - 1} + 1}$

Maximus George 2022-01-21

Evaluate $\sum_{k = 1}^{\infty} \frac{k^{2}}{(k - 1)!}$

Joan Thompson 2022-01-19

How can we prove that?
$\sum_{n = 1}^{\infty} \frac{x^{3 n}}{(3 n - 1)!} = \frac{1}{3} e^{\frac{- x}{2}} x (e^{\frac{3 x}{2}} - 2 \sin (\frac{π + 3 \sqrt{3} x}{6}))$

jamessinatraaa 2022-01-19

How can I evaluate
$\sum_{n = 1}^{\infty} \frac{2 n}{3^{n + 1}}$

Mary Hammonds 2022-01-19

How do I prove:
$lim_{n \to + \infty} \sqrt[n]{n!}$ is infinte?

Chris Cruz 2022-01-19

How to find infinite sum How to find infinite sum
$1 + \frac{1}{3} + \frac{1 \cdot 3}{3 \cdot 6} + \frac{1 \cdot 4 \cdot 5}{3 \cdot 6 \cdot 9} + \frac{1 \cdot 3 \cdot 5 \cdot 7}{3 \cdot 6 \cdot 9 \cdot 12} + \dots$

Joanna Benson 2022-01-18

How to show the following equality?
$\sum_{n = 0}^{\infty} \frac{1}{a^{2} + n^{2}} = \frac{1 + a π \coth a π}{2 a^{2}}$

Sandra Allison 2022-01-18

Test the condition for convergence of
$\sum_{n = 1}^{\infty} \frac{1}{n (n + 1) (n + 2)}$
and find the sum if it exists.

Sandra Allison 2022-01-18

Can you please explain why
$\sum_{k = 1}^{\infty} \frac{k}{2^{k}} = 2$

Daniell Phillips 2022-01-18

Find the sum:
$S = \sum_{k = 1}^{\infty} \frac{1}{k^{2} - a^{2}}$
where $a \in (0, 1)$

Roger Smith 2022-01-17

Calculate: $\lim_{n \to \infty} e^{- n} \sum_{k = 0}^{n} \frac{n^{k}}{k!}$

Madeline Lott 2022-01-17

Whats

compagnia04 2022-01-17

How to prove:
$\sum_{n = 0}^{\infty} \frac{n^{2}}{2^{n}} = 6$

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