Detailed Explanations for Calculus 2 Equations

For what values of $a > 0$ is the equation
$\sum_{n = 1}^{\infty} \frac{2}{{(n - 0.5)}^{2} + a} = \frac{π}{\sqrt{a}}$
true ?

Nyah Conrad 2022-02-27

Study the behaviour of
$\sum_{n = 1}^{\infty} \frac{n + \log (n)}{{(n + \cos (n))}^{3}}$

sacateundisco8i3 2022-02-27

If $\frac{1}{200} \sum_{n = 1}^{399} \frac{5^{200}}{5^{n} + 5^{200}} = \frac{a}{b}$ , then find $| a - b |$

An object is moving along the curve = . When the object passess through the point (9,3), its x-coordinate increases at a rate of 2 m/s. How fast is the distance from the object to the origin changing at this instant?

ymhonnolfq 2022-02-26

What function does $\sum_{n = 0}^{\infty} \frac{{(- 1)}^{n} (2 n)!}{(1 - 2 n) n!^{2} 4^{n}} \frac{x^{n}}{y^{2 n}}$ correspond to?

Jupellodseple804 2022-02-26

I have to prove
$\frac{\sin (n θ)}{\sin (θ)} = 2^{n - 1} \prod_{k = 1}^{n - 1} (\cos (θ) - \cos (\frac{π k}{n}))$

OIPLZLqm6 2022-02-26

I want to know how to compute the closed form for the series
$\sum_{n = 0}^{\infty} \frac{(2 n)!}{{(n!)}^{2}} {(\frac{| A |}{2})}^{2 n}, | A | < 1,$

Arslan Lyons 2022-02-26

What is $S_{m} (n)$ if $S_{0} (n) = 1$ and $S_{m + 1} (n) = \sum_{k = 1}^{n} S_{m} (k)$ and m and n are integers?

SnuluddidaPalbx4 2022-02-26

Value of $\sum_{n = 0}^{1947} \frac{1}{2^{n} + \sqrt{2^{1947}}}$ ?

Zaccagliaodi 2022-02-26

Evaluate:
$\sum_{n = 1}^{\infty} \frac{n^{2} + 1}{n \cdot 2^{n - 1}}$

Carole Juarez 2022-02-26

I have to prove the following:
$\int_{0}^{1} \frac{x^{\frac{1}{3}}}{1 - x} \log \frac{1}{x} d x = \sum_{n = 0}^{\infty} \frac{9}{{(3 n + 4)}^{2}}$

Myah Fuller 2022-02-26

Find convergence of:
$\sum_{n = 1}^{\infty} \frac{1}{{(n!)}^{\frac{2}{n}}}$

Nettie Potts 2022-02-26

How should I prove convergence using Cauchy sequences
$\sum_{k = 1}^{n} \frac{\sin (k^{3} + 1)}{(4 k + 1) (4 k + 5)}$

simnelsbl4 2022-02-26

Determine the convergence of
$\sum_{n = 1}^{+ \infty} \int_{0}^{\frac{1}{n}} \frac{\sin x}{1 + x} d x$

leciazyg 2022-02-25

Show that :
$\sum_{m = 1}^{\infty} \sum_{n = 2^{m - 1}}^{2^{m} - 1} \frac{m}{(2 n + 1) (2 n + 2)} = 1 - γ$

Olivia Vasquez 2022-02-25

That is equivalent to
$π = \sqrt{12} \sum_{n \geq 0} \frac{(- 1)^{n}}{3^{n} (2 n + 1)}$

Kris Patton 2022-02-25

Find the value of
$\sum_{n = 0}^{\infty} \frac{1}{9 n^{2} + 9 n + 2}$

Alexandria Dodd 2022-02-25

Proving that:
$\frac{3}{2} \sum_{k = 1}^{\infty} \frac{4}{k^{3} + k^{2}} = π^{2} - 6$

erycletrefeebr 2022-02-25

Find the sum:
$\sum_{k = 0}^{\infty} {(- 2)}^{k} \frac{k + 2}{k + 1} x^{k}$

Adrienne Rowe 2022-02-25

Does the sum $\sum_{n = 1}^{\infty} \frac{\sqrt{n!}}{(3 + \sqrt{1}) (3 + \sqrt{2}) \dots (3 + \sqrt{n})}$ converge or diverge?

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