Geometric series partial sums question

[cue928]

I am looking at a geometric series problem that has already been worked out, so not assigned, but I do not see where they get a number:

Summation from n=1 to inf: 1/(n^2+4n+3)
In doing the partial sums, he has (1/2)* summation... 1/(i+1) - 1/(i+3)
I understand the breakup, but where does the "1/2" come from?

 

[micromass]

Because

\frac{1}{n+1}-\frac{1}{n+3}=\frac{2}{n^2+4n+3}

But you want a 1 in the numerator...