$\begin{array}{l} a)A = \frac{1}{2} + \frac{1}{{{2^2}}} + \frac{1}{{{2^3}}} + ... + \frac{1}{{{2^{49}}}} + \frac{1}{{{2^{50}}}}\\ \Rightarrow 2A = 1 + \frac{1}{2} + \frac{1}{{{2^2}}} + ... + \frac{1}{{{2^{49}}}}\\ \Rightarrow 2A - A = A = 1 - \frac{1}{{{2^{50}}}} < 1\\ Vậy\,A < 1\\ b)B = \frac{1}{3} + \frac{1}{{{3^2}}} + ... + \frac{1}{{{3^{100}}}}\\ \Rightarrow 3B = 1 + \frac{1}{3} + ... + \frac{1}{{{3^{99}}}}\\ \Rightarrow 2B = 1 - \frac{1}{{{3^{100}}}}\\ \Rightarrow B = \frac{1}{2} - \frac{1}{{{{2.3}^{100}}}} < \frac{1}{2}\\ c)TT:C < \frac{1}{3} \end{array}$