How do you use the ratio test to test the convergence of the series #∑(4^n) /( 3^n + 1)# from n=1 to infinity?
1 Answer
Apr 5, 2016
Use the ratio test to find that this series diverges...
Explanation:
Let
Then:
#a_(n+1)/a_n = (4^(n+1)/(3^(n+1)+1))/(4^n/(3^n + 1))#
#=(4^(n+1)(3^n+1))/(4^n(3^(n+1)+1))#
#=4/3*(1+3^-n)/(1+3^(-n-1))#
So
Since this is greater than