Find a closed form for these summations?

Question

Find a closed form for these summations?

    n=10000
    ∑ i
    i=1

Answer 1

This is the series 1 + 2 + 3 + 4 + ... + 10000, or stated in words, the sum of the first 10000 integers.

 

There's a simple rule for this sum:  n(n+1)/2, where n is the number of integers you're counting.  Try it for the first few values of n and see that it works.

 

So the answer would be 10000(10001)/2 = 50005000.