Need to know if Series converges, and the sum

Evaluate ` sum_(n=0)^(oo)(n!)/(1000^n) `

This series diverges. We use the ratio test:

` lim_(n->oo)(((n+1)!)/(1000^(n+1)))/((n!)/(1000^n)) `

`=lim_(n->oo)((n+1)!)/(1000^(n+1))*(1000^n)/(n!) `

`=lim_(n->oo)n/1000=oo `

Since the limit of the ratio is greater than 1, the series diverges.

Comments

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