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?

1 Answer
Oct 17, 2015

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.