tìm x biết 1/51+1/52+1/53+…+1/100=x^2-3/1.2+x^2-3/3.4+…+x^2-3/99.100

0 bình luận về “tìm x biết 1/51+1/52+1/53+…+1/100=x^2-3/1.2+x^2-3/3.4+…+x^2-3/99.100”

1. Đáp án: $x=\pm2$

   Giải thích các bước giải:

   Ta có :
   $\dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=\dfrac{x^2-3}{1.2}+\dfrac{x^2-3}{3.4}+…+\dfrac{x^2-3}{99.100}$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)(\dfrac{1}{1.2}+\dfrac{1}{3.4}+…+\dfrac{1}{99.100})$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)(\dfrac{2-1}{1.2}+\dfrac{4-3}{3.4}+…+\dfrac{100-99}{99.100})$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)(\dfrac11-\dfrac12+\dfrac13-\dfrac14+..+\dfrac1{99}-\dfrac1{100})$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)((\dfrac11+\dfrac13+\dfrac15+..+\dfrac1{99})-(\dfrac12+\dfrac14+..+\dfrac1{100}))$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)((\dfrac11+\dfrac12+\dfrac13+\dfrac14+\dfrac15+..+\dfrac1{99}+\dfrac1{100})-2(\dfrac12+\dfrac14+..+\dfrac1{100}))$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)((\dfrac11+\dfrac12+\dfrac13+\dfrac14+\dfrac15+..+\dfrac1{99}+\dfrac1{100})-(\dfrac11+\dfrac12+..+\dfrac1{50}))$

   $\to \dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100}=(x^2-3)(\dfrac{1}{51}+\dfrac{1}{52}+…+\dfrac{1}{100})$

   $\to x^2-3=1$
   $\to x^2=4$
   $\to x=\pm2$

   Bình luận