Roman C. answered • 04/02/16

Masters of Education Graduate with Mathematics Expertise

We can break this down to quickly writing down the first few terms in three sequences.

Let A

_{j}= ∑_{k=1,...,j}1 = j, B_{j}= ∑_{j=1,...,i}A_{j}, C_{n}= ∑_{I=1,...,n}B_{i}.Then we want an n such that C

_{n}= 220.A's: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

B's: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

C's: 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, ...

The we see that C

_{10}= 220, so n=10.