I wasn't sure where to place this problem in the forums. I hope this area is OK. I'm trying to find a pattern in this series of numbers. How can I find a simplified expression, where I evaluate it at my given n, and the proper f(n) is returned?

n=4, f(4)=6

n=5, f(5)=10

n=6, f(6)=15

n=7, f(7)=21

I found that the function can be represented by the sum

.

So for n=4, f(4)=3+2+1

n=5, f(5)=4+3+2+1

...

Is there a way I can find a simplified expression? For example, the series

2,4,8,16 can be represented by n^2. I was curious if I can find a simplified expression for this pattern.

Thanks

Edit: This should probably be moved to the number theory forum. Sorry