Interesting Sequence
Algebra
Level
3
Consider the sequence \(\left\{a_{n}\right\}\) where \(a_{1}=0\) and \(a_{n+1}=a_{n}+1+2\sqrt{1+a_{n}}\) for natural numbers \(n\).
Find the value of \(a_{2009}\).
by
Jerry Han Jia Tao