Question

Tính nhanh: \(A=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+...+\frac{1}{9999}\)

Answer 1

\(A=1/3.5+1/5.7+1/7.9+…+1/99.101\)

A.2=2/3.5+2/5.7+2/7.9+…+2/99.101

A.2=1/3-1/5+1/5-1/7+1/7-1/9+...+1/99-1/101

Vậy

A.2=1/3-1/101=98/303

A=98/303/2=49/303

Đúng không

Answer 2

A = 1/15 + 1/35 + 1/63 + 1/99 + ... + 1/9999

   = 1/3x5 + 1/5x7 + 1/7x9 + 1/9x11 + ... + 1/99x101

A x 2 = 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 + ... + 2/99x101

         = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + ... + 1/99 - 1/101

         = 1/3 - 1/101 = 98/303

Vậy A = 98/303 : 2 = 49/303