Question

1/1x2x3+1/2x3x4+....+1/18x19x20

mọi người giúp mình với ạ

 

Answer 1

\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{18.19.20}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{18.19.20}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}.\dfrac{2}{1.3}+\dfrac{1}{3}.\dfrac{2}{2.4}+...+\dfrac{1}{19}.\dfrac{2}{18.20}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{18.19}-\dfrac{1}{19.20}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{19.20}\right)=\dfrac{1}{4}-\dfrac{1}{19.40}=\dfrac{189}{760}\)

Answer 2

help me , please