x-1/2 + x-1/6 + x-1/12 + x-1/20 +…+ x-1/9900 =19/20

Bởi

x-1/2 + x-1/6 + x-1/12 + x-1/20 +…+ x-1/9900 =19/20

0 bình luận về “x-1/2 + x-1/6 + x-1/12 + x-1/20 +…+ x-1/9900 =19/20”

  1. Đáp án: x = $\frac{97}{4950}$ 

     

    Giải thích các bước giải:

    x – $\frac{1}{2}$ + x – $\frac{1}{6}$ + x – $\frac{1}{12}$ + x – $\frac{1}{20}$ + ….. + x – $\frac{1}{9900}$ = $\frac{19}{20}$ 

    ( x + x + x + x + ….. + x ) – ( $\frac{1}{2}$ + $\frac{1}{6}$ + $\frac{1}{12}$ + $\frac{1}{20}$ + ….. + $\frac{1}{9900}$ ) = $\frac{19}{20}$ 

    ( x + x + x + x + ….. + x ) – ( $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + ….. + $\frac{1}{99.100}$ ) = $\frac{19}{20}$ 

    x . 99 – ( 1 – $\frac{1}{2}$ + $\frac{1}{2}$ – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{4}$ + $\frac{1}{4}$ – $\frac{1}{5}$ + ….. + $\frac{1}{99}$ – $\frac{1}{100}$ ) = $\frac{19}{20}$ 

    x . 99 – ( 1 – $\frac{1}{100}$ ) = $\frac{19}{20}$ 

    x . 99 – $\frac{99}{100}$ = $\frac{19}{20}$ 

    x . 99 = $\frac{19}{20}$ + $\frac{99}{100}$

    x . 99 = $\frac{97}{50}$ 

    x = $\frac{97}{50}$ : 99

    x = $\frac{97}{4950}$ 

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