# Welcome 2016

Algebra Level 4

If $$\displaystyle \sum_{r=1}^\infty \dfrac r{r^4+r^2+1} = 1 - \dfrac1a$$, find the number of digits in $$a^{2016}$$.

You are given the following approximations: $$\log 10 = 1, \log 5 = 0.6990, \log 3 = 0.4771$$.

×