Review question

What's the sum of the $r^{th}$ bracket in $(1), (2,3), (4,5,6),\cdots$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7240

Suggestion

The positive integers are bracketed as follows: $(1), (2,3), (4,5,6),\dotsc ,$ where there are $r$ integers in the $r^{th}$ bracket.

Find expressions for the first and last integers in the $r^{th}$ bracket.

Can we find a pattern for the starting terms in the brackets? For the finishing terms?

Prove that the sum of the integers in the $r^{th}$ bracket is $\dfrac{1}{2}r(r^2+1)$.

Can we use the values for the first and the last integers in the $r^{th}$ bracket from the first part?