Question

H=\(\dfrac{0,25}{1x2}\)+\(\dfrac{0,25}{2x3}\)+......+\(\dfrac{0,25}{199x200}\)

Answer 1

\(H=0,25\times\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{19\times20}\right)\)

\(=0,25\times\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\)

\(=0,25\times\left(1-\dfrac{1}{20}\right)=0,25\times\dfrac{19}{20}=\dfrac{19}{80}\)

Answer 2

\(H=\dfrac{0.25}{1\cdot2}+\dfrac{0.25}{2\cdot3}+...+\dfrac{0.25}{199\cdot200}\)

\(=\dfrac{1}{4}\cdot\dfrac{199}{200}=\dfrac{199}{800}\)