Skipping over the busy-work

Many people know this math problem, but I'm going to post it here anyway, because I've always liked the solution.

Add numbers 1 through 100.

Of course, you could just go through and add...

1+2=3

3+3=6

6+4=10

10+5=15*

... but that would be a lot of busy-work, and mathematicians don't approve of busy-work. 

*One small cool thing about the sequence you get from going through and adding everything (1, 3, 6, 10, 15, 21, 28...): these are the triangular numbers. 

So how can you do this in a much faster, easier, and more effective way?

To find the answer, go to answersdiscarded.blogspot.com. As usual, this is where I beg you to try to figure it out by yourselves before checking the answer.

If you've already done that problem, do this one:
Add all numbers divisible by three from 100 to 200.