We want to complete the formula.
∑_(i=1)^ni =
This is the sum of the first n terms of an arithmetic series.
1, 2, 3, ..., n-1, n
We can pair up the first term of this sequence with the last term, the second term with the one before last and so on.
1, 2, 3, ..., n-2, n-1, n
The sum of each pair is n+1.
1 + n = n+1 2+ n-1=n+1 3+ n-2=n+1 ...
The sum of all n terms is the number of pairs multiplied by the sum of each pair n+1. The number of pairs is half of the number of terms, n2. Let's find the sum!
∑_(i=1)^ni = n(n+1)/2
