vazelinahS
2021-11-02
Answered

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.

$10-2+0.4-0.008+\dots$

You can still ask an expert for help

unessodopunsep

Answered 2021-11-03
Author has **105** answers

Geometric series:

Where r and a are constants

If |r|<1, then the series converges to

This is a geometric series with common ration

Since

Sum of the geometric series is

The series converges to

asked 2021-12-20

Which of the answers is an arithmetic sequence?

a) 2, 4, 8, 16, 32

b) 3, 6, 9, 15, 24

c) 2, 5, 7, 12, 19

d). 6, 13, 20, 27, 34

a) 2, 4, 8, 16, 32

b) 3, 6, 9, 15, 24

c) 2, 5, 7, 12, 19

d). 6, 13, 20, 27, 34

asked 2021-03-18

Find the radius of convergence, R, of the series.

$\sum _{n=1}^{\mathrm{\infty}}\frac{(2x+9{)}^{n}}{{n}^{2}}$

Find the interval, I, of convergence of the series.

Find the interval, I, of convergence of the series.

asked 2020-10-19

a) Find the Maclaurin series for the function

$f(x)=\frac{1}{1}+x$

b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function

$g(x)=\frac{1}{(x+1{)}^{2}}$

c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function

$h(x)=\frac{1}{(x+1{)}^{3}}$

d) Find the sum of the series

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

This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is$\frac{7}{2}$

b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function

c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function

d) Find the sum of the series

This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is

asked 2021-11-03

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 3-4+16/3-64/9+........

asked 2022-01-22

Let x be any positive real number, and define a sequence $\left[{a}_{n}\right]$ by

$a}_{n}=\frac{\left[x\right]+\left[2x\right]+\left[3x\right]+\dots +\left[nx\right]}{{n}^{2}$

where$\left[x\right]$ is the largest integer less than or equal to x. Prove that $\underset{n\to \mathrm{\infty}}{lim}{a}_{n}=\frac{x}{2}$

where

asked 2021-02-20

Given series:

$\sum _{k=3}^{\mathrm{\infty}}[\frac{1}{k}-\frac{1}{k+1}]$

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.

asked 2021-02-05

The terms of a series are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning.

$\sum _{n=1}^{\mathrm{\infty}}{a}_{n}$

${a}_{1}=\frac{1}{5},\text{}{a}_{n+1}=\frac{\mathrm{cos}n+1}{n}{a}_{n}$