y = 1/10 + 1/15 + 1/21 + ... + 1/120
1/2y = 1/20 + 1/30 + 1/42 + ... + 1/240
1/2y = 1/4x5 + 1/5x6 + 1/6x7 + ... + 1/15x16
1/2y = 1/4 -1/5 + 1/5 - 1/6 + 1/6 -1/7 + ... +1/15 -1/16
1/2y = 1/4 - 1/16
1/2y = 3/16
y = 3/16 : 1/2
y = 3/16 x 2
y= 3/8
\(y=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(y=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(y=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(y=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(y=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(y=2.\frac{3}{16}\)
\(y=\frac{3}{8}\)
\(\Rightarrow y=2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+.........+\frac{1}{240}\right)\)
\(\Rightarrow y=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+.............+\frac{1}{15.16}\right)\)
\(\Rightarrow y=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...........+\frac{1}{15}-\frac{1}{16}\right)\)
\(\Rightarrow y=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(\Rightarrow y=2.\frac{3}{16}\)
\(\Rightarrow y=\frac{3}{8}\)
