Tính :
A=\(\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+......+\dfrac{1}{120}\)
B=\(\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+......+\dfrac{4}{107.111}\)
C=\(\dfrac{7}{10.11}+\dfrac{7}{11.12}+\dfrac{7}{12.13}+......+\dfrac{7}{69.70}\)
D=\(\dfrac{15}{90.94}+\dfrac{15}{94.98}+\dfrac{15}{98.102}+......+\dfrac{15}{146.150}\)
\(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{120}\)
\(A=\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+...+\dfrac{2}{240}\)
\(A=\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}+...+\dfrac{2}{15.16}\)
\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)
\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(A=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)
\(A=2.\dfrac{3}{16}\)
\(A=\dfrac{3}{8}\)
\(B=\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+...+\dfrac{4}{107.111}\)
\(B=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{107}-\dfrac{1}{111}\)
\(B=\dfrac{1}{3}-\dfrac{1}{111}\)
\(B=\dfrac{12}{37}\)
\(C=\dfrac{7}{10.11}+\dfrac{7}{11.12}+\dfrac{7}{12.13}+...+\dfrac{7}{69.70}\)
\(C=7\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{7}{69.70}\right)\)
\(C=7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
\(C=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)\)
\(C=7.\dfrac{3}{35}\)
\(C=\dfrac{3}{5}\)
\(D=\dfrac{15}{90.94}+\dfrac{15}{94.98}+\dfrac{15}{98.102}+...+\dfrac{15}{146.150}\)
\(D=\dfrac{1}{4}.15\left(\dfrac{4}{90.94}+\dfrac{4}{94.98}+\dfrac{4}{98.102}+...+\dfrac{4}{146.150}\right)\)
\(D=\dfrac{15}{4}\left(\dfrac{1}{90}-\dfrac{1}{94}+\dfrac{1}{94}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{102}+...+\dfrac{1}{146}-\dfrac{1}{150}\right)\)
\(D=\dfrac{15}{4}\left(\dfrac{1}{90}-\dfrac{1}{150}\right)\)
\(D=\dfrac{15}{4}.\dfrac{1}{225}\)
\(D=\dfrac{1}{60}\)