What is the formula for Sum of Series?

Question

I forgot this formula and am trying to calculate some odds for a physics project and it would help me out a lot to figure this out..

Sorry I should have been more specific.. I was looking for arithmitic Sum of Series.
Example: What is a formula I could use to figure out 1+2+3+4...999+1000

Answer 1

Arithmetic Series
First term = a
Common difference = d
Number of terms = n
Sn = a + (a + d) + (a + 2d) -----+[ a + (n - 1)d ]
reverse equation:-
Sn = [ a + (n -1) d ] + ---(a + d) + a
Add the two equations:-
2Sn = n [ 2a + (n - 1) d ]
Sn = (n / 2) [ 2a + (n - 1) d ]
n = 100 , a = 1,d = 1
S100 = 50 [2 + 99 ]
S100 = 50 x 101
S100 = 5050

Answer 2

1+2+3+4+...+n=n(n+1)/2


2+4+6+8+...+2n
=2(1+2+3+....+n)
=2* (n)(n+1)/2
=n(n+1)



1^2+2^2+3^2+4^2+...+n^2
=n(n+1)(2n+1)/6

Answer 3

you should mension what type of series i.e arithmatic of geometric or something else.