Sequences and series

Question 1

sigma 1

Answer 1

n

Question 2

sigma r

Answer 2

1/2n(n+1)

Question 3

sigma r^2

Answer 3

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

Question 4

sigma r^3

Answer 4

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

Question 5

relationship between sigma r and sigma r3

Answer 5

sigma r3 = sigma r squared

Question 6

expansion of sigma r

Answer 6

1/2n^2 + 1/2n

Question 7

sigma r^2 expansion

Answer 7

2/6n^3 + 1/2n^2 + 1/6n

Question 8

sigma r^3 expanded

Answer 8

1/4n^4 + 1/2n^3 + 1/4n^2

Question 9

r2 + r3 + r4

Answer 9

1/12n(n+1) (6 + 2(2n+ 1) + 3n(n+1))

Question 10

how to induct

Answer 10

1 - base where n = 1
2 - assume where n = k
3 - induct where n = k + 1 following from step 2
4 - conclude - since true if n=1, if true for n=k then true for n=k+1 so true for all positive integers n