\(C=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{18}}=1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}+...+\dfrac{1}{131072}-\dfrac{1}{262144}=1+1-\dfrac{1}{262144}=2-\dfrac{1}{262144}\)
A = \(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+...+\dfrac{3}{17\cdot20}=\dfrac{1}{3}\cdot\left(\dfrac{3}{2}-\dfrac{3}{5}+\dfrac{3}{5}-\dfrac{3}{8}+...+\dfrac{3}{17}-\dfrac{3}{20}\right)=\dfrac{1}{3}\cdot\left(\dfrac{3}{2}-\dfrac{3}{20}\right)=\dfrac{1}{3}\cdot\dfrac{27}{20}=\dfrac{9}{20}\)
\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{12}}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}...+\dfrac{1}{2048}-\dfrac{1}{4096}=1-\dfrac{1}{4096}=\dfrac{4095}{4096}\)
