What is the sum from n=1 to infinity of 1/n+1/(n!) ?

The sum from n=1 to infinity of 1/n+1/(n!) is diverges

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sum from n=1 to infinity of 1/n+1/(n!)

n = 1 \sum \infty \frac{1}{n} + \frac{1}{n !}

diverges

Solution steps

n = 1 \sum \infty \frac{1}{n} + \frac{1}{n !}

Apply Series Comparison Test:

diverges

= diverges

n = 2 \sum \infty \frac{3}{n ^{2} + n - 2}

n = 1 \sum \infty \frac{n}{9 ^{n}}

n = 4 \sum \infty \frac{3}{n ( n - 1 )}

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

What is the sum from n=1 to infinity of 1/n+1/(n!) ?
The sum from n=1 to infinity of 1/n+1/(n!) is diverges