3 - Series

Question 1

What formula do you use for the sum of a series of constant terms?

Answer 1

n
Σ1 = n
r = 1

Question 2

What is the formula for the sum of the first n natural numbers?

Answer 2

n
Σr = 1/2n(n+1).
r=1

Question 3

What if the series does not start at r = 1?

Answer 3

n n k-1
Σf(r) = Σf(r) - Σf(r).
r=k r=k r=1

Question 4

How is this rearranged:

n
Σkf(r)
r = 1

Answer 4

n
kΣf(r)
r=1

Question 5

What is this equal to:

n
Σ(f(r) + g(r))
r=1

Answer 5

n n
Σf(r) + Σg(r)
r=1 r=1

Question 6

What is the formula for the sum of the squares of the first n natural numbers?

Answer 6

n
Σr^2 = 1/6n(n + 1)(2n + 1)
r=1

Question 7

What is the formula for the sum of the cubes of the first n natural numbers?

Answer 7

n
Σr^3 = 1/4n^2(n + 1)^2.
r=1