Calculus Examples of Geometric Series and More

How could we prove this ?
$\sum_{i = 1}^{n} (i^{2} + 3 i + 1) \times i! = (n + 3) \times (n + 1)! - 3$

basura8w081 2022-03-23

Let's say for example these two:
$\frac{3 n}{2 n + 3} {(- 1)}^{n + 1} - \frac{{(- 1)}^{n}}{2 n} {({(- 1)}^{n} + \frac{1}{n})}^{2}$

juctommaccedo662f 2022-03-22

Solve the series:
$lim_{n \to \infty} \frac{k + 1}{3^{k}}$

Neveah Stewart 2022-03-19

Calculate sum of an infinite series
$\sum_{n = 1}^{\infty} {(- 1)}^{n - 1} n^{2} x^{n}$

2selz76t 2022-03-18

Determine a series of transformations that would map Figure P onto Figure Q.

ransomedv37 2022-03-15

Are there any generalisations of the identity $\sum_{k = 1}^{n} k^{3} = {(\sum_{k = 1}^{n} k)}^{2}$ ?

e3r6a2n1dz60 2022-03-15

Are there any other ways to demonstrate that
$\sin (x) = \sum_{k = 0} \frac{{(- 1)}^{k} x^{1 + 2 k}}{(1 + 2 k)!}$

arrostetzwyl 2022-03-14

What is the sum of the series $\sum_{k = 1}^{\infty} - \frac{1}{2^{k} - 1}$

Alexis Garner 2022-03-12

What would be the radius of convergence of $\sum_{n = 0}^{\infty} z^{3^{n}}$ ?

Shyla Singleton 2022-03-11

Which values for a will make series convergent or divergent?
$\sum_{k = 1}^{\infty} \frac{1}{(2 k + 1) \ln^{a} (2 k + 1)}$

Brittney Cuevas 2022-03-02

A bit rusty on this stuff. The whole problem is proving this is true:
$2 \leq 1 + \sum_{m = 1}^{n} \frac{1}{m!} \leq 1 + \sum_{m = 1}^{n} \frac{1}{2^{m - 1}} < 3$

Scoopedepalj 2022-02-28

Why is:
$\sum_{k = 1}^{[\frac{n}{2}]} \sin^{2} ((2 k - 1) \frac{π}{n}) = \frac{n}{4}$

Lubna Boyce 2022-02-28

I am given the series
$\sum_{n = 1}^{\infty} \frac{n^{n - 1}}{{(2 n^{2} + n + 1)}^{(n + \frac{1}{2})}}$

Beverley Rahman 2022-02-28

What is the convergence rate of the tail of the series
$a_{n} = \sum_{k > n} exp (- p k) k {(\log k)}^{2}$

Guy Rollins 2022-02-28

Can be series $\sum_{r = 0}^{\infty} \frac{e^{- r}}{1 + r}$ be further simplified?

Theresa Chung 2022-02-28

Let $f : R \to R$ be continuous and bounded. Prove that for each $x > 0$ we have
$e^{- n x} \cdot \sum_{k = 0}^{\infty} \frac{{(n x)}^{k}}{k!} f (\frac{k}{n}))$

Cormac Gilbert 2022-02-28

Check the convergence or divergence of the series
$\sum_{n = 2}^{\infty} {(- 1)}^{n} (\frac{1}{\log n} + \frac{\cos n}{n^{2}})$

trasdulaive 2022-02-28

I have the following series:
$\sum_{n = 1}^{\infty} (2^{\frac{1}{n}} + 2^{- \frac{1}{n}} - 2)$

beuz89100g6c 2022-02-28

Prove: the complex series $\sum_{n = 0}^{\infty} (\frac{z^{n + 1}}{n + 1} - \frac{2 z^{2 n + 3}}{2 n + 3})$ is discontinuous at $z = 1$ .

Vofteldetgpt 2022-02-28

Calculate:
$\sum_{n = 0}^{\infty} n {(\frac{4}{5})}^{n + 1}$

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