# Sequences in Sequences

Define the sequence recursively by and

Find an explicit formula for in terms of n.

- 14 August, 2012 -
- Article, Math Problems -
- Tags : algebra, analysis, titu
- 0 Comments

Since this recurrence isn’t linear in , we define a subsequence to get rid of that square root in the hopes that the resulting sequence can be expressed as a linear recurrence.

We now construct a closed form expression for

Therefore, we see by construction that .