25. Calculate the sum of $n$ terms of the series $1+\frac{3}{2}+\frac{5}{4}+\frac{9}{8}+\ldots$
25. Each term of the sum can be represented as $\frac{2^{n-1}+1}{2^{n-1}}$.

Then $S=1+\frac{2+1}{2}+\frac{2^{2}+1}{2^{2}}+\ldots+\frac{2^{n-1}+1}{2^{n-1}}=n+1-\frac{1}{2^{n-1}}$.