This series fails the first test: .
sum (n+1)/(n+2) as n goes from 1 to infinity
my solution:
let {Xn}= (n+1) /(n+2)
for large n , the series is approx. to 1
where sum 1 is divergent.
so i am going to show that {Xn} >= C .1 where C is a constant
in fact, n+1>n and n+2=< 3n
so Xn=(n+1)/(n=2)> n/3n=(1/3) . 1
since sum 1 diverges, so does sum (1/3).1
so by comparison test, sum Xn is divergent.
is my proof correct? anybody help me? many thanks~!