Question

Tìm x biết:

\(\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right).x=1\)

Các bạn giúp nhé

Answer 1

\(\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)x=1\)

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

\(\left(\frac{1}{2}-\frac{1}{50}\right)x=1\)

\(\frac{13}{25}x=1\)

\(x=1:\frac{13}{25}=\frac{25}{13}\)

Answer 2

( 1/2x3 +1/3x4 + ... + 1/49x50 ) x X = 1

( 3-2/2x3 + 4-3/3x4 + ... + 50-49/49x50 ) x X = 1

( 1/2 -1/3 + 1/3 - 1/4 + ... + 1/49 - 1/50 ) x X = 1

( 1/2 - 1/50 ) x X = 1

12/25 x X = 1

X = 1 : 12/25

X = 25/12

Answer 3

Ta có: \(\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right).x=1.\)

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

    \(\Rightarrow\left(\frac{1}{2}-\frac{1}{50}\right).x=1\)

     \(\Rightarrow\frac{12}{25}x=1\)

      \(\Rightarrow x=1:\frac{12}{25}=\frac{25}{12}\)

Vậy x = \(\frac{25}{12}\)