Summation of Series

Question 1

n
Σ 1 = ?
r=1

Answer 1

n

Question 2

n
Σ r = ?
r=1

Answer 2

1/2 n (n+1)

Question 3

n
Σ r^2 = ?
r=1

Answer 3

1/6 n (n+1) (2n+1)

Question 4

n
Σ r^3 = ?
r=1

Answer 4

1/4 n^2 (n+1)^2

Question 5

Method of differences

Answer 5

Substitute in numbers, n, and n+1
Most terms will cancel
Expand and simplify what you are left with

Question 6

How do you workout what it will tend to as n tends to ∞?

Answer 6

Substitute n for really large numbers and look at what the answer is close to