Question
The sum of $n$ terms of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\ldots$(A) $2^{n}-n-\frac{1}{2}$(B) $1-2^{-n}$(C) $n+2^{-n}-1$(D) $\frac{1}{2}\left(2^{n}-1\right)$
Step 1
Step 1: We can rewrite each term in the series as follows: \[\frac{1}{2}=1-\frac{1}{2}, \frac{3}{4}=1-\frac{1}{4}, \frac{7}{8}=1-\frac{1}{8}, \frac{15}{16}=1-\frac{1}{16}, \ldots\] Show more…
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