How do you use the limit comparison test on the series #sum_(n=2)^oosqrt(n)/(n-1)# ?
1 Answer
Jul 29, 2015
The series diverges.
Explanation:
Note first that we can write:
In the limit, the terms 'act like'
# = lim_(nrarroo) (sqrt(n+1)sqrtn)/n#
# = lim_(nrarroo) sqrt(n^2+n)/n#
# = lim_(nrarroo) (nsqrt(1+(1/n)))/n#
# = 1#
Since