FM - Core Pure 1 - 3) Series

Question 1

Formula to find sum of a series that doesn’t start at r=1

Answer 1

Σⁿ_r=k f(r) = Σⁿ_r=1 f(r) - Σ^k-1_r=1 f(r)

Question 2

Rearrange Σⁿ_r=1 kf(r)

Answer 2

kΣⁿ_r=1 f(r)

Question 3

Rearrange Σⁿ_r=1 (f(r) + g(r))

Answer 3

Σⁿ_r=1 f(r) + Σⁿ_r=1 g(r)

Question 4

Formula for sum of a series of constant terms

Answer 4

Σⁿ_r=1 1 = n

Question 5

Formula for sum of the first n natural numbers

Answer 5

Σⁿ_r=1 r = n/2(n+1)