Question

\(\frac{2}{2x3}+\frac{2}{3x4}+\frac{2}{4x5}+...+\frac{2}{49x50}\)

Answer 1

\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{49.50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{49}\right)-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}=\frac{12}{25}\)

~ Hok tốt ~

Answer 2

\(\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{49.50}\)

\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{50}\right)=2.\frac{12}{25}=\frac{24}{25}\)

Answer 3

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{50}\right)\\ =2.\frac{12}{25}\\ =\frac{24}{50}\)

Answer 4

\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{49.50}\)

\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{50}\right)\)

\(=2.\frac{12}{25}\)

\(=\frac{24}{25}\)

Study well ! >_<

Answer 5

2/2.3+2/3.4+....+2/49.50

=2(1/2.3+1/3.4+.....+1/49.50)

=2(1/2-1/50)

=2.12/25

=24/15