Question

hay giup minh voi

B=1/2*x+1/2+1/6+1/12+...+1/9900=2

Answer 1

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

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

  =\(\frac{1}{2.x}+\left(1-\frac{1}{100}\right)\)\(=2\)

  =\(\frac{1}{2.x}+\frac{99}{100}\)\(=2\)

  =\(\frac{1}{2.x}=2-\frac{99}{100}\)

  =\(\frac{1}{2.x}=\frac{101}{200}\)

  =\(2.x=200\)

  =\(x=200:2=100\)

Answer 2

1/2 * x + 1/2 + 1/6 + 1/12 + .... + 1/9900 = 2 

<=> 1/2 * x + ( 1/2 + 1/6 + 1/12 + ... + 1/9900 ) = 2 

<=> 1/2 * x + ( 1 /1.2 + 1/2.3 + 1/3.4 + ... + 1/99.100 ) = 2

<=> 1/2 * x + ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/99 - 1/100 ) = 2 

<=> 1/2 * x + ( 1 - 1/100 ) = 2 

<=> 1/2 * x + ( 100/100 - 1/100 ) = 2 

<=> 1/2 * x + 99/100 = 2 

<=> 1/2 * x = 2 - 99/100 

<=> 1/2 * x = 101/100

<=> x = 101/100 : 1/2

<=> x = 101/100 * 2 

<=> x = 101/50

Vậy x = 101/50 

Answer 3

x=100