$a_n=a_{n-1}\displaystyle \frac{n+1}{n}$ if $n > 1$
$a_n=1$ if $n=1$
I'm not too sure where to start here. This is part of a review for a class and I can't really seem to remember what we're reviewing. The first 5 values are...
$a_1 = 1,a_2=1.5,a_3=2,a_4=2.5,a_5=3$
Sums of these to each point....
$a_1=1, a_2=2.5, a_3=4.5, a_4=7, a_5=10$
It doesn't seem like it should be too tricky to figure out how to get a formula for a sum of the first N terms, since each term seems to just increase by 0.5 every team, I just haven't done this for a while and am a little rusty. Any pointers would be greatly appreciated!