Question

tìm x biết (1/1*2 + 1/2*3 + 1/3*4 + ... + 1/99*100) - 2x =1/2

Answer 1

\(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)-2x=\dfrac{1}{2}\)

\(\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)-2x=\dfrac{1}{2}\)

\(\left(1-\dfrac{1}{100}\right)-2x=\dfrac{1}{2}\)

\(\dfrac{99}{100}-2x=\dfrac{1}{2}\)

2x = \(\dfrac{99}{100}-\dfrac{1}{2}=\dfrac{49}{100}\)

x = \(\dfrac{49}{100}:2=\dfrac{49}{200}\)

Answer 2

\(\dfrac{49}{200}\)