Originally Posted by

**clarinetqueen92** A partial sum is taking all integers (to infinity) plugging them into an equation, and adding each term together. I started with a table, and tried to find some sort of pattern by subtraction between each term, but got nowhere fast.

Gee, I thought the partial sum was the result of adding the first n terms of the series

$\displaystyle s_n=a_1+a_2+a_3+\dots+a_{n-2}+a_{n-1}+a_n=\sum_{k=1}^n\,a_k$

or was I wrong about that?

If I'm right, then $\displaystyle a_1=s_1=3-(1^{-1})=2$$\displaystyle a_2=s_2-s_1=3-(2^{-2})-2=3-\frac{1}{4}-2$

etc.