Question

1/1×2 + 1/2×3+1/3×4+...+1/49×50

 

Answer 1

1/1x2 + 1/2x3 + 1/3x4 + ... + 1/49x50

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/49 - 1/50

= 1 - 1/50

= 49/50

Answer 2

Đặt dãy trên là A

Ta có:

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

Answer 3

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

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

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

Answer 4

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

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

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

\(\frac{49}{50}\)