# Arithmetic Sequences

Find a closed form formula for the sequence {1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,…}

- 6 August, 2012 -
- Article, Math Problems -
- Tags : 104 problems, number theory, titu
- 0 Comments

Looking at the ‘s associated with the boxed ‘s, we see that for the boxed numbers, . For example

This naturally produces lower and upper bounds on the range of for some particular .

(1)

Because monotonically increases, by bounding the for the , we’ll have successively shown that our expression satisfies the problem, we only need to show that