Question

1/1x2 + 1/2x3 +...+ 1/49x50 = ?

Answer 1

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}=\frac{49}{50}\)

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}...\frac{1}{49.50}\)

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

\(=\frac{1}{1}-\frac{1}{50}\)

\(=\frac{49}{50}\)