ka1leE

2020-10-20

Show that the series converges. What is the value of the series?

$\sum _{n=2}^{\mathrm{\infty}}(-\frac{5}{3}{)}^{n}(\frac{2}{5}{)}^{n+1}$

ensojadasH

Skilled2020-10-21Added 100 answers

We have to Show that the series converges. What is the value of the series?

Series is given below:

We will use geometric series test .

Geometriic series test says if series of the form

Work is shown below:

Now compare the given series to geometric series and find value of r .

If

In this case

After that find value of a (starting term of series).

With the help of a, r and sum of geometric series formula we will find sum.

Work is shown below:

Previous step continue

Answer

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

What is the derivative of the work function?

How to use implicit differentiation to find $\frac{dy}{dx}$ given $3{x}^{2}+3{y}^{2}=2$?

How to differentiate $y=\mathrm{log}{x}^{2}$?

The solution of a differential equation y′′+3y′+2y=0 is of the form

A) ${c}_{1}{e}^{x}+{c}_{2}{e}^{2x}$

B) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{3x}$

C) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{-2x}$

D) ${c}_{1}{e}^{-2x}+{c}_{2}{2}^{-x}$How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate $\sqrt{xy}=x-2y$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given $1+\frac{2}{3}+\frac{4}{9}+...$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?

A. 4.2

B. 4.4

C. 4.7

D. 5.1What is the derivative of $\frac{x+1}{y}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving $f\left(x\right)={e}^{2-x},x\in [1,2]$ around the x axis?

How to differentiate ${x}^{\frac{2}{3}}+{y}^{\frac{2}{3}}=4$?

The differential coefficient of $\mathrm{sec}\left({\mathrm{tan}}^{-1}\left(x\right)\right)$.