Question

B=1/10+1/15+1/21+...+1/120

Answer 1

\(\frac{1}{2}B=\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\)

\(\frac{1}{2}B=\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\)

\(\frac{1}{2}B=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\)

\(\frac{1}{2}B=\frac{1}{4}-\frac{1}{16}=\frac{3}{16}\Rightarrow B=\frac{3}{16}:\frac{1}{2}=\frac{3}{8}\)

Answer 2

\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(B=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)

\(B=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(B=2\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(B=2.\frac{3}{16}=\frac{6}{16}=\frac{3}{8}\)

Answer 3

\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(\Rightarrow\frac{1}{2}B=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\)

\(\Rightarrow\frac{1}{2}B=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\)

\(\Rightarrow\frac{1}{2}B=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\)

\(\Rightarrow\frac{1}{2}B=\frac{1}{4}-\frac{1}{16}\)

\(\Rightarrow\frac{1}{2}B=\frac{3}{16}\)

\(\Rightarrow B=\frac{3}{16}\div\frac{1}{2}\)

\(\Rightarrow B=\frac{3}{8}\)