Question

A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely.

Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3

Answer 1

@satellite73 @sami-21 @jim_thompson5910

Answer 2

To find Sk, replace every 'n' with 'k'

Answer 3

Do the same to find Sk+1

Answer 4

Let me know what you get

Answer 5

sk [k(k + 1)(k + 2)]/3
sk+1 [k+1(k+1 + 1)(k+1 + 2)]/3

Answer 6

@jim_thompson5910

Answer 7

More like this

Sk: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + k(k + 1) = [k(k + 1)(k + 2)]/3

Answer 8

Sk+1: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + (k+1)(k+1 + 1) = [(k+1)(k+1 + 1)(k+1 + 2)]/3

You'll need to simplify the above

Answer 9

k(k + 1) = [k(k + 1)(k + 2)]/3