Question

\(\dfrac{1}{50}-\dfrac{1}{50.49}-\dfrac{1}{49.48}-...-\dfrac{1}{2.1} \)

Answer 1

=1/50-(1-1/2+1/2-1/3+...+1/49-1/50)

=1/50-1+1/50

=1/25-1=-24/25

Answer 2

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{1}{50}-\dfrac{1}{50\cdot49}-\dfrac{1}{49\cdot48}-...-\dfrac{1}{2\cdot1}\)

`=`\(\dfrac{1}{50}-\left(\dfrac{1}{50\cdot49}+\dfrac{1}{49\cdot48}+...+\dfrac{1}{2\cdot1}\right)\)

`=`\(\dfrac{1}{50}-\left(\dfrac{1}{50}-\dfrac{1}{49}+\dfrac{1}{49}-\dfrac{1}{48}+...+\dfrac{1}{2}-1\right)\)

`=`\(\dfrac{1}{50}-\left(\dfrac{1}{50}-1\right)\)

`=`\(\dfrac{1}{50}-\left(-\dfrac{49}{50}\right)\)

`= 1`