The positive integers are bracketed as follows:

(1), (2,3), (4,5,6), . . .

where there are r integers in the rth bracket. Prove that the sum of the integers in the rth bracket is

this is what I did

using the formula for arithmetic sequence,

we know that there are r integers. and the difference is 1

so that becomes

Sum of r integers = where a is the first term of the sequence

However, I can't figure out what a (a.k.a the first term) is equal to

any ideas?

thanks