twaal22: What is 1+2+3+4+5....+401?
CPhill's way is really good but if you are learning about APs and GPs at school maybe you are meant to do it that way.
Have you learned about arithmentic progressions (APs) yet?
1,2,3,4,....... is an arithmetic progression because you have to keep adding the same number each time to get the next term.
You keep adding 1. The common difference d=1
The first term a = 1
Now the sum of the first n terms of an AP is
S
n = n/2(a+L)
or alternatively
S
n = n/2(2a+(n-1)d)
You can use either of these formulas, you are probably suppose to memorise them. I'm going to use the first one.
S
401 = 401/2(1+401) => 401/2 * 402 = 401*201 = 80601
+129852 
+118677 
