A = 1/10 + 1/15 + 1/21 + ... + 1/120
A = 2/20 + 2/30 + 2/42 + ... + 2/240
A = 2 × (1/4×5 + 1/5×6 + 1/6×7 + ... + 1/15×16)
A = 2 × (1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/15 - 1/16)
A = 2 × (1/4 - 1/16)
A = 2 × (4/16 - 1/16)
A = 2 × 3/16
A = 3/8
\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+.....+\frac{1}{120}\)
\(2xA=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+.....+\frac{2}{240}\)
\(=2x\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\right)\)
\(=2x\left(\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}+....+\frac{1}{15x16}\right)\)
\(=2x\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(=2x\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(=2x\left(\frac{4}{16}-\frac{1}{16}\right)\)
\(=2x\frac{3}{16}\)
\(=\frac{3}{8}\)
\(=>A=\frac{3}{8}:2=\frac{3}{8}x\frac{1}{2}=\frac{3}{16}\)
Vậy \(A=\frac{3}{16}\)
