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  4. If bn=((1/5)) log √5((1/4)+(1/8)+(1/16)+ ldots+(1/4 ⋅ 2n-1)), find ([ displaystyle lim n arrow ∞(bn)]+3).

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

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Solution:

Correct answer is '5'