she has not seen such a boat for ages (ago)

-- the last time ..............

Ta có:

\(B=\frac{1}{2}+\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{99}\)

\(=2^{-1}+2^{-2}+2^{-3}+...+2^{-99}\)

\(\Rightarrow2B=1+2^{-1}+2^{-2}+...+2^{-98}\)

\(\Rightarrow2B-B=\left(1-2^{-99}\right)+\left(2^{-1}-2^{-1}\right)+\left(2^{-2}-2^{-2}\right)+...+\left(2^{-98}+2^{-98}\right)\)

\(\Rightarrow B=1-\frac{1}{2^{99}}\)

mà \(\frac{1}{2^{99}}>0\Rightarrow1-\frac{1}{2^{99}}< 1\Rightarrow B< 1\left(đpcm\right)\)