Question

consider the statement: 2+6+12+…+n(n+1)=(n(n+1)(n+2))/3. Show that the statement is true when n=1

Answer 1

this appears to be the start of mathematical induction

so the 1st term is 2 this is when n = 1

to check use the general term n(n + 1) let n = 1 1(1+1) = 2

then \[\frac{n(n + 1)(n+2)}{3} \]

is the sum of the 1st n terms

so let n = 1 substitute it in the sum formula above and see if you get 2.

then the sum of 1 term will be equal to the 1st term