tính nhanh nhất có thể 1/2 + 1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

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1. Đáp án: $\frac{9}{10}$ 

    

   Giải thích các bước giải:

   $\frac{1}{2}$ + $\frac{1}{6}$ + $\frac{1}{12}$ + $\frac{1}{20}$ +$\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$ + $\frac{1}{72}$ + $\frac{1}{90}$ 

   = $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + $\frac{1}{5.6}$ + $\frac{1}{6.7}$ + $\frac{1}{7.8}$ + $\frac{1}{8.9}$ + $\frac{1}{9.10}$

   = 1 – $\frac{1}{2}$ + $\frac{1}{2}$ – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{4}$ + $\frac{1}{4}$ – $\frac{1}{5}$ + $\frac{1}{5}$ – $\frac{1}{6}$ + $\frac{1}{6}$ – $\frac{1}{7}$ + $\frac{1}{7}$ – $\frac{1}{8}$ + $\frac{1}{8}$ – $\frac{1}{9}$ + $\frac{1}{9}$ – $\frac{1}{10}$

   = $\frac{1}{1}$ – $\frac{1}{10}$ 

   = $\frac{10}{10}$ – $\frac{1}{10}$ 

   = $\frac{9}{10}$ 

    

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2. `1/2 +1/6 +1/12 +1/20 +1/30 +1/20 + 1/42 + 1/56 +1/72 +1/90`

   `1/(1.2) +1/(2.3) +1/(3.4) +1/(4.5) + 1/(5.6) +1/(6.7) +1/(7.8) +1/(8.9) +1/(9.10)`

   `=1- 1/2 +1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +1/5 -1/6 +1/6 -1/7 +1/7 -1/8 +1/8 -1/9 +1/9 -1/10`

   `=1+(1/2- 1/2)+(1/3- 1/3)+(1/4- 1/4)+(1/5 -1/5)+(1/6 -1/6)+(1/7 -1/7)+(1/8 -1/8)+(1/9 -1/9)- 1/10`

   `=1+0+0+0+0+0+0+0+0 -1/10`

   `=1- 1/10`

   `=10/10 -1/10`

   `=9/10`

   chúc học tốt

    

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