Question

1___1.2+1___2.3+1____3.4+....+1_49.50 <1

Answer 1

\(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+...+\dfrac{1}{49x50}\)< 1

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

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

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

Answer 2

\(\Rightarrow\dfrac{49}{50}< 1\)