Question

D= 2/(1.3) + 2/(3.5) + ... + 2/(97.99)

Answer 1

\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{97\cdot99}\)

\(=\left(2-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{97}-\frac{2}{99}\right):2\)

\(=\left(2-\frac{2}{99}\right):2=\frac{98}{99}\)

Answer 2

D = 1 - 1/3 + 1/3 - 1/5 + .... + 1/97 - 1/99

D = 1 - 1/99

D = 98/99