Question

Determine the convergence or divergence of the series. sum_{n=1}^infty(1+frac{1}{n})^n

Series
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asked 2020-12-09
Determine the convergence or divergence of the series.
\(\sum_{n=1}^\infty(1+\frac{1}{n})^n\)

Answers (1)

2020-12-10
The given series is
\(\sum_{n=1}^\infty(1+\frac{1}{n})^n\)
To test the convergence or divergence first apply series divergence test.
if \(\lim_{n\to\infty}a_n\) does not exist or \(\lim_{n\to\infty}a_n\ne0\Rightarrow\sum_{n=1}^\infty\) diverges
here apply series divergence test
\(\lim_{n\to\infty}(1+\frac{1}{n})^n=e\)
Since the limit is not equal to zero
\(\sum_{n=1}^\infty(1+\frac{1}{n})^n\) diverges
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