Question

How do you use the ratio test to test the convergence of the series `∑ (-5)^(n+1)n / 2^n` from n=1 to infinity?

Answer 1

See the explanation.

Explanation:

`L=lim_(n->oo)|a_(n+1)/a_n|`

`L=lim_(n->oo) |((-5)^(n+2)(n+1)/2^(n+1))/((-5)^(n+1)n/2^n)|`

`L=lim_(n->oo) |(-5) (n+1)/(2n)|= 5lim_(n->oo) (n+1)/(2n)=5/2`

`L>1` so the series is divergent.