giúp mk vs mai mk nộp rùi :< A=1/1.3+1/3.5+.......+1/2019.2021 B=1/4.7+1/7.10+.....+1/65.68

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1. Đáp án:

    

   Giải thích các bước giải:

   A= $\frac{1}{1.3}$+$\frac{1}{3.5}$+….+$\frac{1}{2019.2021}$  

     =$\frac{1}{1}$-$\frac{1}{3}$+$\frac{1}{3}$-$\frac{1}{5}$+….+ $\frac{1}{2019}$-$\frac{1}{2021}$

     =1-$\frac{1}{2021}$

     =$\frac{2021}{2021}$-$\frac{1}{2021}$=$\frac{2020}{2021}$ 

   B=$\frac{1}{4.7}$+$\frac{1}{7.10}$+….+$\frac{1}{65.68}$

     =$\frac{1}{4}$-$\frac{1}{7}$+$\frac{1}{7}$-$\frac{1}{10}$+….+ $\frac{1}{65}$-$\frac{1}{68}$         =$\frac{1}{4}$-$\frac{1}{68}$  

    =$\frac{17}{68}$-$\frac{1}{68}$=$\frac{16}{68}$  

   Trả lời

2. $\text{Áp dụng công thức:}$`a/(n.(n+a))=1/n-1/(n+a)`
   `A=1/1.3+1/3.5+…….+1/2019.2021`
   `A=1/2(2/1.3+2/3.5+…….+2/2019.2021)`
   `A=1/2(1-1/3+1/3-1/5+…+1/2019-1/2021)`
   `A=1/2(1-1/2021)`
   `A=1/2(2021/2021-1/2021)`
   `A=1/2. 2020/2021`
   `A=1010/2021`
   `B=1/4.7+1/7.10+…+1/65.68`
   `B=1/3(3/4.7+3/7.10+…+3/65.68)`
   `B=1/3(1/4-1/7+1/7-1/10+…+1/65-1/68)`
   `B=1/3(1/4-1/68)`
   `B=1/3(17/68-1/68)`
   `B=1/3. 4/17`
   `B=4/51`

    

   Trả lời