Detailed Explanations for Calculus 2 Equations

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

Beverley Rahman 2022-02-23

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

Zeenat Horn 2022-02-23

Consider, for all $n \in N$ :
$u_{n} = \int_{0}^{1} (1 - {(1 - t^{n})}^{\frac{1}{n}}) d t$
Does the series $\sum_{n \geq 1} u_{n}$ converges ?

haugmbd 2022-02-23

Evaluate:
$lim_{n \to \infty} \sum_{k = 1}^{n} \frac{1}{n + \sqrt{k^{2} + n}}$

klancimarsn 2022-02-23

Prove
$\frac{3 π}{8} = \sum_{k \geq 0} {(- \frac{1}{5})}^{k} \frac{F_{2 k + 1}}{2 k + 1} q^{2 k + 1}$
where $q = \frac{2 + 2 \sqrt{2}}{1 + \sqrt{\frac{17 + 8 \sqrt{2}}{5}}}$ , and $F_{n}$ are the Fibonacci numbers.

Ivor Schofield 2022-02-23

How can you derive that
$\sum_{n = 1}^{\infty} \frac{n}{3^{n}} = \frac{3}{4}$ ?

Carole Juarez 2022-02-23

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

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More