chứng minh rằng 1-1/12+1/3-1/4+1/5-1/6+…+1/99-1/100=1/51+1/52+..+1/100

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1. Giải thích các bước giải:

   Ta có :
   $\dfrac{1}{1}-\dfrac12+\dfrac13-\dfrac14+\dfrac15-\dfrac16+…+\dfrac1{99}-\dfrac{1}{100}$ 

   $=(\dfrac{1}{1}+\dfrac13+..+\dfrac1{99})-(\dfrac12+\dfrac14+\dfrac16+…+\dfrac{1}{100})$ 

   $=(\dfrac{1}{1}+\dfrac13+..+\dfrac1{99})+(\dfrac12+\dfrac14+\dfrac16+…+\dfrac{1}{100})-2(\dfrac12+\dfrac14+\dfrac16+…+\dfrac{1}{100})$ 

   $=(\dfrac{1}{1}+\dfrac12+\dfrac13+..+\dfrac1{99}+\dfrac{1}{100})-(\dfrac11+\dfrac12+\dfrac13+…+\dfrac{1}{50})$ 

   $=\dfrac1{51}+\dfrac{1}{52}+…+\dfrac{1}{100}$

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