Question

Câu hỏi : Tính nhanh tổng sau :

  A= 1/1.2 + 1/2.3 + 1/3.4 +....+ 1/49.50

 GIÚP IK MN 

Answer 1

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=1-\frac{1}{50}=\frac{49}{50}\)

Answer 2

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{49\cdot50}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=1-\frac{1}{50}=\frac{50-1}{50}=\frac{49}{50}\)

Answer 3

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}=\frac{49}{50}\)

Answer 4

A=1-1/2+1/2-1/3+.....+1/49-1/50

=1-1/50

=49/50

Vậy......

Answer 5

Trả lời:

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

    \(=\)\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)   

    \(=1-\frac{1}{50}\)

      \(=\frac{49}{50}\)

Vậy \(A=\frac{49}{50}\)