What is the sum from n=0 to infinity of (n!)/(n!+1) ?

The sum from n=0 to infinity of (n!)/(n!+1) is diverges

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sum from n=0 to infinity of (n!)/(n!+1)

n = 0 \sum \infty \frac{n !}{n ! + 1}

diverges

Solution steps

n = 0 \sum \infty \frac{n !}{n ! + 1}

Apply Series Divergence Test:

diverges

= diverges

k = 1 \sum \infty 5 (- \frac{1}{8})^{5 k}

n = 1 \sum \infty 5 (0.3)^{n - 1}

n = 1 \sum \infty cos (5 n)

n = 0 \sum \infty \frac{1}{7 - n}

n = 1 \sum \infty n e^{- 2 n^{2}}

What is the sum from n=0 to infinity of (n!)/(n!+1) ?
The sum from n=0 to infinity of (n!)/(n!+1) is diverges