Using the integral test, how do you show whether #sum (n + 2) / (n + 1)# diverges or converges from n=1 to infinity?
1 Answer
Jul 4, 2015
The series diverges.
Explanation:
Without the integral test:
The terms do not go to
If we must use the integral test let's do so as quickly as possible.
# = lim_(brarroo) (x+ln abs(x+1))]_1^b#
# = lim_(brarroo)[ (b+ln(b+1)) - (1+ln2)]#
# = oo + oo -1-ln2 = oo#
The series diverges.