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

for \(S_k\) replace every \(n\) by \(k\)

Answer 2

So.... 60.. i am not understanding how u replace n by k

Answer 3

the answer is not a number
write down exactly what you see written above, but instead of putting an \(n\) put a \(k\)

Answer 4

the left hand side of the equal sign will be
\[1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + k(k + 1) \]

Answer 5

so unless this is it im still confused..Sk: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + k(k + 1) = [k(k + 1)(k + 2)]/3

Answer 6

ok

Answer 7

yes, exactly

Answer 8

thank you

Answer 9

then for the next one, replace all the \(n\)'s by \(k+1\) make sure to use parentheses and the distributive law when you simplify

Answer 10

ok thank you