1. ## comparison 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~!

2. This series fails the first test: $\frac{{n + 1}}{{n + 2}} \to 1 \ne 0$.

3. thanks. i know that is the simplest way to do.
but now i am asked to use the comparison test, is my solution correct? Thanks

4. $\left( {\forall n} \right)\left[ {\frac{{n + 1}}
{{n + 2}} > \frac{1}
{2}} \right]$
so $\sum\limits_{n = 1}^K {\frac{{n + 1}}
{{n + 2}}} > \frac{K}{2}$
.
Make $K$ as large as needed.