Tính nhanh phân số

Question

1/20+1/30+1/42+ ... +1/50+1/990

Answer 1

\(A=\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+…+\dfrac{1}{9900}\\A=\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+…+\dfrac{1}{99.100}\\A=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+…+\dfrac{1}{99}-\dfrac{1}{100}\\A=\dfrac{1}{4}-\dfrac{1}{100}\\A=\dfrac{1}{25}\) Đã sửa đề nha có vài chỗ bị sai đó

Answer 2

A=1/4*5 + 1/5*6 + 1/6*7 +.....+1/99*100

A=1/4-1/5+1/5-1/6+1/6-1/7+...+1/99-1/100

A=1/4-1/100

A=25/100-1/100

A=6/25