Question

1/2.3+1/3.4+...+1/99.100

Answer 1

\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

= \(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}\)+...+\(\dfrac{1}{99}-\dfrac{1}{100}\)

= \(\dfrac{1}{2}-\dfrac{1}{100}\)

= \(\dfrac{49}{100}\)

Answer 2

\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+....+\dfrac{1}{99.100}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(=\dfrac{1}{2}-\dfrac{1}{100}\)

\(=\dfrac{49}{100}\)