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 3011 views around the world You can reuse this answer Creative Commons License