## Challenge #4

Another sequence-related challenge for your sequencing pleasure. For those of you in my Elementary Functions class, this is extra credit. (Hence, if you post a comment with your solutions, please refrain from posting an explanation along with it.)

1. Find the sum of the first 500 terms of this series:

$1 + 3 + 7 + 12 + 19 + 27 + 37 + 48 + \cdots$

2. Find the sum of the first 100 terms:

$\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \cdots$