A Lucas Sum

Algebra Level 5

Let p=1+1+1+p = \sqrt{1+\sqrt{1+\sqrt{1+\ldots}}}.

The sum

k=2pk2k\sum_{k=2}^{\infty} \frac{\lfloor p^{k} \rceil}{2^{k}}

can be expressed as ab\frac{a}{b} for a,ba,b coprime, where \lfloor \cdot \rceil denotes the nearest integer function. Find a+ba+b.

×

Problem Loading...

Note Loading...

Set Loading...