Question

cho B=1/1.2.3+1/2.3.4+1/3.4.5+...1/7.8.9+1/8.9.10

Answer 1

\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+..+\frac{1}{7.8.9}+\frac{1}{8.9.10}\)

\(B=2\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(B=2\times\left(1-\frac{1}{10}\right)\)

\(B=2\times\frac{9}{10}\)

\(B=\frac{9}{5}\)

Answer 2

\(B=2\times\left(\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+\frac{1}{3\times4}-\frac{1}{4\times5}+..+\frac{1}{9\times10}\right)\)

\(B=2\times\left(\frac{1}{1\times2}-\frac{1}{9\times10}\right)\)

\(B=2\times\frac{22}{45}\)

\(B=\frac{44}{45}\)