\(\displaystyle{\sum_{{{x}={1}}}^{\infty}}\frac{1}{{8}^{n}}\)converges when \({8}^{{-{n}}}={0}\)

asked 2021-09-03

\({\sum_{{{x}={1}}}^{\infty}}\frac{{{n}+{6}}}{{{n}^{2}+{12}{n}+{8}}}\)

asked 2021-11-23

Find whether the series diverges and its sum:

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\left(-{1}\right)}^{{{n}+{1}}}{\frac{{{3}}}{{{5}^{{n}}}}}\)

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\left(-{1}\right)}^{{{n}+{1}}}{\frac{{{3}}}{{{5}^{{n}}}}}\)

asked 2021-11-13

Determine the sum of the following series.

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\left({\frac{{{1}^{{n}}+{9}^{{n}}}}{{{11}^{{n}}}}}\right)}\)

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\left({\frac{{{1}^{{n}}+{9}^{{n}}}}{{{11}^{{n}}}}}\right)}\)

asked 2021-10-24

Test the series for convergence or divergence.

\(\displaystyle{\sum_{{{n}={0}}}^{\infty}}{\frac{{{\left(-{1}\right)}^{{{n}+{1}}}}}{{\sqrt{{{n}+{4}}}}}}\)

\(\displaystyle{\sum_{{{n}={0}}}^{\infty}}{\frac{{{\left(-{1}\right)}^{{{n}+{1}}}}}{{\sqrt{{{n}+{4}}}}}}\)

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 2021-11-08

Approximate the sum of the series correct to four decimal places.

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

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

asked 2021-09-02

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

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

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