Question

A= 1/1.2 + 1/2.3+1/3.4+...+ 1/49.50

Answer 1

A = 1- 1/2 + 1/2-1/3 +1/3-1/4+...........+ 1/49-1/50

A= 1- 1/50= 49/50

Answer 2

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

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

\(A=\frac{1}{1}-0+0+0+0+......+0+0-\frac{1}{50}\)

\(A=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)