Formula to find the sum of a series of constant terms:
ⁿ∑r=1 1 = n
Formula to find the sum of the series that does not start at 1:
ⁿ∑r=k f(r) = ⁿ∑r=1 f(r) - k-1∑r=1 f(r)
Formula for the sum of the first natural numbers:
ⁿ∑r=1 r = ½n(n + 1)
Formula for the sum of the squares of the first n natural numbers is:
ⁿ∑r=1 r² = 1/6n(n + 1)(2n + 1)
Formula for the sum of the cubes of the first n natural numbers is:
ⁿ∑r=1 r³ = ¼n²(n + 1)²
Rearrange ⁿ∑r=1 k f(r) , with k being a constant:
k ⁿ∑r=1 f(r)
Rearrange ⁿ∑r=1 (f(r) + g(r)) :
ⁿ∑r=1 f(r) + ⁿ∑r=1 g(r)