floymdiT
2020-10-23
Answered

Use the Limit Comparison Test to determine the convergence or divergence of the series.

$\sum _{n=1}^{\mathrm{\infty}}\frac{1}{{n}^{2}({n}^{2}+4)}$

You can still ask an expert for help

okomgcae

Answered 2020-10-24
Author has **93** answers

We have to find the given series is convergence or divergence.

Limit comparison test:

Suppose that we have two series

Then, if

We have given

Let

Then,

And suppose

Then,

And

Now,

Since, series

Therefore, given series is convergent.

Jeffrey Jordon

Answered 2021-12-27
Author has **2262** answers

Answer is given below (on video)

asked 2022-01-24

Show that:

$\underset{n\to \mathrm{\infty}}{lim}\frac{\sum _{k=1}^{n}\frac{1}{k}}{\mathrm{ln}\left(n\right)}=1$

asked 2022-05-02

Second Order Differential Equations $ay{}^{\u2033}+b{y}^{\prime}+cy=0$ , without complex numbers

asked 2021-12-07

Equation of a line and a line segment Let $ell$ be the line that passes through the points ${P}_{0}(-3,\text{}5,\text{}8)$ and ${P}_{1}(4,\text{}2,\text{}-1)$ .

a. Find an equation of$ell$ .

b. Find parametric equations of the line segment that extends from$P}_{0$ to $P}_{1$ .

a. Find an equation of

b. Find parametric equations of the line segment that extends from

asked 2022-05-03

Series solution of $x{y}^{{}^{\u2033}}+2{y}^{{}^{\prime}}-xy=0$

I get$r(r+1)=0,(r+1)(r+2){c}_{1}=0$ and

$c}_{n+1}=\frac{{c}_{n-1}}{(n+1+r)(n+r+2)$

The first equation gives the indicial roots$r=-1$ and $r=0$ . The case for $r=0$ is fine.

For$r=-1$ , I don't see how ${c}_{1}=0$ is implied by the second equation. The way I see it, since $1+r=0$ when $r=-1,{c}_{1}$ is not necessarily zero here, but this leads to a different solution to what is in the text book. What am I missing? Why is $c}_{1$ forced to be zero?

I get

The first equation gives the indicial roots

For

asked 2021-10-24

Test the series for convergence or divergence.

$\sum _{n=0}^{\mathrm{\infty}}\frac{{(-1)}^{n+1}}{\sqrt{n+4}}$

asked 2021-11-16

Indicate whether the statement is true or false, and if itis false, provide a correct statement. The derivative of a vector-valued function is the slope of the tangent line, just as in the scalar case.

asked 2021-02-03

Given the series:

$9+\frac{117}{4}+\frac{1521}{16}+\frac{19773}{64}+...$

does this series converge or diverge? If the series converges, find the sum of the series.

does this series converge or diverge? If the series converges, find the sum of the series.