Kaycee Roche

2020-12-09

Determine the convergence or divergence of the series.

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

delilnaT

Skilled2020-12-10Added 94 answers

The given series is

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

To test the convergence or divergence first apply series divergence test.

if$\underset{n\to \mathrm{\infty}}{lim}{a}_{n}$ does not exist or $\underset{n\to \mathrm{\infty}}{lim}{a}_{n}\ne 0\Rightarrow \sum _{n=1}^{\mathrm{\infty}}$ diverges

here apply series divergence test

$\underset{n\to \mathrm{\infty}}{lim}(1+\frac{1}{n}{)}^{n}=e$

Since the limit is not equal to zero

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

To test the convergence or divergence first apply series divergence test.

if

here apply series divergence test

Since the limit is not equal to zero

Jeffrey Jordon

Expert2021-12-27Added 2575 answers

Answer is given below (on video)