If you look at the original post, he's really talking about sequences, not series.

There's not a whole lot of difference between taking the limit of a sequence and a function. Since you know limits for functions, you should be able to evaluate

in the cases

,

, and

. When x is negative, there are some difficulties with the definition of

, but since you know n is an integer, it just breaks up into the two cases n odd or n even.

For the Fibonacci sequence, you can prove the formula

by just checking the first two terms and the recurrence relation. Then you can see that

.

- Hollywood