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? Calculus Tests of Convergence / Divergence Ratio Test for Convergence of an Infinite Series 1 Answer Sasha P. 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. Answer link Related questions How do you know when to use the Ratio Test for convergence? How do you use the Ratio Test on the series sum_(n=1)^oon^n/(n!) ? How do you use the Ratio Test on the series sum_(n=1)^oo(n!)/(100^n) ? How do you use the Ratio Test on the series sum_(n=1)^oo(-10)^n/(4^(2n+1)(n+1)) ? How do you use the Ratio Test on the series sum_(n=1)^oo9^n/n ? How do you use the ratio test to test the convergence of the series ∑ 3^n/(4n³+5) from n=1 to... How do you use the ratio test to test the convergence of the series sum_(n=1)^oo((x+1)^n) / (n!) ? How do you use the ratio test to test the convergence of the series ∑3^k/((k+1)!) from n=1 to... How do you use the ratio test to test the convergence of the series ∑(2k)!/k^(2k) from n=1 to... How do you use the ratio test to test the convergence of the series ∑(4^n) /( 3^n + 1) from... See all questions in Ratio Test for Convergence of an Infinite Series Impact of this question 3267 views around the world You can reuse this answer Creative Commons License