Detailed Explanations for Calculus 2 Equations

How do I find:
$\prod_{n = 1}^{\infty} (1 + \frac{1}{π^{2} n^{2}})$

Miguel Davenport 2022-01-23

For $x > 0$ and $y > x + 1$ , how do we prove that
$\sum_{n = 1}^{\infty} \frac{x (x + 1) \dots (x + n - 1)}{y (y + 1) \dots (y + n - 1)} = \frac{x}{y - x - 1}$

siutulysr5 2022-01-23

Evaluate
$\sum_{n, k} \frac{1}{(\begin{matrix} n \\ k \end{matrix})}$
where the summation ranges over all positive integers n, k with $1 < k < n - 1$

Nylah Church 2022-01-23

How to calculate $\int_{0}^{1} x^{x} d x$ using series? I read from a book that
$\int_{0}^{1} x^{x} d x = 1 - \frac{1}{2^{2}} + \frac{1}{3^{3}} + \dots + {(- 1)}^{n} \frac{1}{{(n + 1)}^{n + 1}} + \dots$

Carly Shannon 2022-01-23

For $a \in R$ , show that $\sum_{k \geq 0} \frac{1}{k^{2} + k - α} = \frac{π}{\sqrt{4 α + 1}} \tan (\frac{1}{2} π \sqrt{4 α + 1})$

Branden Valentine 2022-01-22

Theres

Jamarion Kerr 2022-01-22

Find the series:
$\sum_{n = 1}^{\infty} ({(1 + \frac{1}{n})}^{n} - e)$

Kasey Haley 2022-01-22

How to find the sum of this series?
$\sum_{k = 0}^{\infty} \frac{2^{k}}{(\begin{matrix} 2 k + 1 \\ k \end{matrix})}$

plorinosakl 2022-01-22

I have some difficulty to prove the following limit:
$lim_{N \to \infty} \sum_{k = 1}^{N} \frac{1}{k + N} = \ln (2)$

kuntungw3 2022-01-22

Evaluate the integral
$\int_{- π}^{π} {| \sum_{n = 1}^{\infty} \frac{1}{2^{n}} e^{\in x} |}^{2} d x$

Jacquelyn Sanders 2022-01-22

How to compute
$\prod_{n = 2}^{\infty} \frac{n^{3} - 1}{n^{3} + 1}$

Octavio Miller 2022-01-22

Evaluate
$\sum_{n = 1}^{\infty} \frac{1}{n^{2} 2^{n}}$

Shamar Padilla 2022-01-22

Does
$\sum_{n = 1}^{\infty} \frac{1}{n^{1 + \frac{1}{n}}}$
converge? If yes, to where?

maliaseth0 2022-01-22

Let x be any positive real number, and define a sequence $[a_{n}]$ by
$a_{n} = \frac{[x] + [2 x] + [3 x] + \dots + [n x]}{n^{2}}$
where $[x]$ is the largest integer less than or equal to x. Prove that $lim_{n \to \infty} a_{n} = \frac{x}{2}$

Sereinserenormg 2022-01-22

Calculate the sun of the infinite series:
$\sum_{n = 0}^{\infty} \frac{n}{4^{n}}$

Elsa Barron 2022-01-22

Show that the following infinite series
$\sum_{i = 1}^{\infty} \frac{f (n)}{n^{2}}$

Jamarion Kerr 2022-01-22

Need to prove the sequence:
$a_{n} = 1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \dots + \frac{1}{n^{2}}$ converges.

licencegpopc 2022-01-22

How to sum this series for $\frac{π}{2}$ directly?
$\frac{π}{2} = \sum_{k = 0}^{\infty} \frac{k!}{(2 k + 1)!}$

mairie0708zl 2022-01-22

Prove that :
$\sum_{k = 0}^{\infty} \frac{{(- 1)}^{k}}{{(2 k + 1)}^{3}} = \frac{π^{3}}{32}$

spiderifilms6e 2022-01-22

Proving that $\frac{π^{3}}{32} = 1 - \sum_{k = 1}^{\infty} \frac{2 k (2 k + 1) ζ (2 k + 2)}{4^{2 k + 2}}$

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