Ramanujan's nested radical is great! (2)
Algebra
Level
5
\[\large \frac{2016\sqrt{2016\sqrt[3]{2016\sqrt[4]{2016\sqrt[5]{2016\cdots}}}}}{\sqrt{2016\sqrt{2016\sqrt{2016\sqrt{2016\sqrt{2016\cdots}}}}}}=2016^{e+x}\]
Find \(x\) which satisfies the above equation.
Hint: Consider the infinite sum series of \(e\)
Clarification: \(e \approx 2.71828\) denotes the Euler's number.
by
Tommy Li