Calculus Examples of Geometric Series and More

Cauchy condensation test - do I have to prove $\sum_{n = 2}^{\infty} \frac{1}{n^{2}}$ converges?

hughy46u 2022-05-24

Examine the uniform convergence of $\sum_{n = 1}^{\infty} \frac{x}{(1 + n x) (1 + (n + 1) x)}$

America Ware 2022-05-23

Let the real sequence $x_{n}$ be given by,
$\sum_{j = 1}^{2 n} \frac{1}{j} - \sum_{j = 1}^{n} \frac{1}{j} .$

Carly Roy 2022-05-23

Does the series $\sum_{n \geq 1} \frac{\cos (n a) \ln (n)}{\sqrt{n}}$ converge?

Marianna Stone 2022-05-22

Suppose:
$\sum_{n = 2}^{\infty} (\frac{1}{n (\ln (n))^{k}}) = \frac{1}{2 (\ln (2))^{k}} + \frac{1}{3 (\ln (3))^{k}} + . . .,$

Loreenwk 2022-05-22

I am trying to show that the series
$\sum_{n = 1}^{\infty} \frac{z^{n - 1}}{(1 - z^{n}) (1 - z^{n + 1})}$

Jaycee Mathis 2022-05-22

How to determine that this series is conditionally convergent?
$\sum_{n = 1}^{\infty} \int_{n}^{n + 1} \frac{\sin π x}{x^{p} + 1} d x, 0 < p \leq 1$

nileteenice 2022-05-22

We were asked to evaluate the following series:
$\sum_{n = 2}^{\infty} 7 * \frac{- 5^{n}}{2^{3 n - 2}}$

Thomas Hubbard 2022-05-22

Test the convergence of the series
$\sum_{n = 1}^{\infty} \frac{n^{n}}{3^{n} n!}$

Loreenwk 2022-05-22

Case:
$\sum_{n = 1}^{\infty} (- 1)^{n + 1} (2 n - 1)$

aniawnua 2022-05-22

What is the asymptotic behavior of the sequence:
$s_{n} = \sum_{k = 1}^{n} k^{1 / 4}$

Pitrellais 2022-05-22

Find values of x where
$\sum_{n = 1}^{\infty} \frac{(- 1)^{n + 1} (x - 2)^{n}}{n 2^{n}}$

Brooke Kramer 2022-05-21

I discovered the following sequence,
$\sum_{k = 1}^{\infty} \frac{\exp (- p k)}{k^{1 - p}}$
where $p \geq 0$

Rachel Villa 2022-05-21

Calculate the sum
$\sum_{n = 1}^{\infty} \frac{(2 n - 1)!!}{(2 n)!! \cdot 2^{n}}$
where $(2 n - 1)!! = 1 \cdot 3 \dots (2 n - 1)$ , $(2 n)!! = 2 \cdot 4 \dots 2 n$

Nicholas Cruz 2022-05-21

Determine whether $\sum_{k = 1}^{\infty} (1 - \cos (\frac{1}{\sqrt{k}}))$ converges or not

Zeihergp 2022-05-20

Let $f_{1} = 1$ , where $n \in N$ . Show that $f_{2 n + 1} = f_{n + 1}^{2} + f_{n}^{2}$

shelohz0 2022-05-20

Determine the limit of the sequence
$(\frac{1 + 2^{k} + 3^{k} + . . . + n^{k}}{n^{k + 1}} - \frac{1}{k + 1})$

Denisse Valdez 2022-05-20

How can I understand this?
$- q \sum_{n = 0}^{\infty} \frac{t^{p + n q}}{p + n q} = \sum_{n = 0}^{q - 1} ω^{- n p} \ln (1 - ω^{n} t)$

zato1kom7 2022-05-20

Solve the limit of $y_{n} = (1 + \frac{1}{n^{3}})^{n^{2}}$

rs450nigglix2 2022-05-20

I wonder is it true that
$(\sum_{n : a_{n} \leq ϵ} a_{n}^{2}) \cdot ϵ^{(- 3 / 2)} stays bounded as ϵ \to 0$
for all $a_{n}$ that satisfies the above conditions.

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