Question

If $b_n={\left(\frac{1}{5}\right)}^{{\log }_{\sqrt{5}}\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots +\frac{1}{4\cdot 2^{n-1}}\right)}$, find $\left(\left[\underset{n\to \infty }{\lim }\left(b_n\right)\right]+3\right)$.

Answer 1

Answer: 5

Correct answer is (e)