\(a=10\)

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

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 2021-11-02

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

\(\displaystyle{10}-{2}+{0.4}-{0.008}+\ldots\)

\(\displaystyle{10}-{2}+{0.4}-{0.008}+\ldots\)

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 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 2021-09-15

Determine whether the series is convergent or divergent.

\(\displaystyle{1}+{\frac{{{1}}}{{{2}\sqrt{{2}}}}}+{\frac{{{1}}}{{{3}\sqrt{{3}}}}}+{\frac{{{1}}}{{{4}\sqrt{{4}}}}}+{\frac{{{1}}}{{{5}\sqrt{{5}}}}}+\dot{{s}}\)

\(\displaystyle{1}+{\frac{{{1}}}{{{2}\sqrt{{2}}}}}+{\frac{{{1}}}{{{3}\sqrt{{3}}}}}+{\frac{{{1}}}{{{4}\sqrt{{4}}}}}+{\frac{{{1}}}{{{5}\sqrt{{5}}}}}+\dot{{s}}\)

asked 2021-09-02

Please justify whether the series converges or diverges, and find sum, if it converges.

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{3}}{{n}^{{2}}}\)

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{3}}{{n}^{{2}}}\)

asked 2021-08-19

Tell whether the series converges or diverges, and find sum, if it converges.

\(\displaystyle{\sum_{{{n}={3}}}^{\infty}}{\left(\frac{{1}}{{{n}–{2}}}–\frac{{1}}{{n}}\right)}\)

\(\displaystyle{\sum_{{{n}={3}}}^{\infty}}{\left(\frac{{1}}{{{n}–{2}}}–\frac{{1}}{{n}}\right)}\)

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