\(a=10\)

\(r=\frac{-4}{10}=\frac{-2}{5}\)

Now sum:

\(S_n=\frac{a}{1-r}\)

\(=\frac{10}{(1+\frac{2}{5})}\)

\(=\frac{50}{7}\)

\(r=\frac{-4}{10}=\frac{-2}{5}\)

Now sum:

\(S_n=\frac{a}{1-r}\)

\(=\frac{10}{(1+\frac{2}{5})}\)

\(=\frac{50}{7}\)

asked 2021-05-12

Determine whether the series is convergent or divergent.

\(1+\frac{1}{2\sqrt2}+\frac{1}{3\sqrt3}+\frac{1}{4\sqrt4}+\frac{1}{5\sqrt5}+\dots\)

\(1+\frac{1}{2\sqrt2}+\frac{1}{3\sqrt3}+\frac{1}{4\sqrt4}+\frac{1}{5\sqrt5}+\dots\)

asked 2021-05-05

Determine if the following series is convergent or divergent

a) \(\sum_{n=2}^{\infty}\frac{1}{n \ln n}\)

b) \(\sum_{n=0}^{\infty} ne^{-n^2}\)

c) \(\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}\)

d)\(\sum_{n=4}^{\infty}\frac{1}{n^7}\)

a) \(\sum_{n=2}^{\infty}\frac{1}{n \ln n}\)

b) \(\sum_{n=0}^{\infty} ne^{-n^2}\)

c) \(\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}\)

d)\(\sum_{n=4}^{\infty}\frac{1}{n^7}\)

asked 2020-10-25

Determine whether the given series is convergent or divergent. Explain your answer. If the series is convergent, find its sum.

\(\sum_{n=0}^\infty\frac{3^n+2^{n+1}}{4^n}\)

\(\sum_{n=0}^\infty\frac{3^n+2^{n+1}}{4^n}\)

asked 2021-03-06

Consider the following series.

\(\sum_{n=1}^\infty\frac{\sqrt{n}+4}{n^2}\)

The series is equivalent to the sum of two p-series. Find the value of p for each series.

Determine whether the series is convergent or divergent.

\(\sum_{n=1}^\infty\frac{\sqrt{n}+4}{n^2}\)

The series is equivalent to the sum of two p-series. Find the value of p for each series.

Determine whether the series is convergent or divergent.

asked 2021-03-08

If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.

asked 2021-06-02

Find the value of x for which the series converges

\(\sum_{n=1}^\infty(x+2)^n\) Find the sum of the series for those values of x.

\(\sum_{n=1}^\infty(x+2)^n\) Find the sum of the series for those values of x.

asked 2020-11-23

Determine if the series \(\displaystyle{\sum_{{{n}={0}}}^{\infty}}{a}_{{n}}\) is convergent or divergent if the partial sum of the n terms of the series is given below. If the series is convergent, determine the value of the series.

\(\displaystyle{S}_{{n}}={\frac{{{5}+{8}{n}^{{2}}}}{{{2}-{7}{n}^{{2}}}}}\)

\(\displaystyle{S}_{{n}}={\frac{{{5}+{8}{n}^{{2}}}}{{{2}-{7}{n}^{{2}}}}}\)

asked 2021-06-13

\(\sum_{n=1}^\infty nx^{n-1},\ |x|<1\)

asked 2021-06-01

asked 2020-11-12

Identify whether the series is an arithmetic series (AS), geometric series (GS) or not one of the difined types ( NASGS ) and determine the sum (for NASGS, write NO SUM). Write your Solution.

a. \(1+\frac32+\frac94+...+\frac{81}{16}\)

a. \(1+\frac32+\frac94+...+\frac{81}{16}\)