bài 1 tính: a) 3/1.4+3/4.7+3/7.10+…..+3/40.43 b) 4/2.4+4/4.6+4/6.8+….+4/2016.2018 c)1/18+1/54+1/108+….+1/990

0 bình luận về “bài 1 tính: a) 3/1.4+3/4.7+3/7.10+…..+3/40.43 b) 4/2.4+4/4.6+4/6.8+….+4/2016.2018 c)1/18+1/54+1/108+….+1/990”

1. Đáp án + Giải thích các bước giải:

   `a)3/1.4+3/4.7+3/7.10+…+3/40.43=1/1-1/4+1/4-1/7+1/7-1/10+…+1/40-1/43=1/1-1/43=43/43-1/43=42/43`

   `b)4/2.4+4/4.6+4/6.8+…+4/2016.2018=2(2/2.4+2/4.6+2/6.8+…+2/2016.2018)=2(1/2-1/4+1/4-1/6+1/6-1/8+…+1/2016-1/2018)=2(1/2-1/2018)=2(1009/2018-1/2018)=2. 504/1009=1008/1009`

   `c)1/18+1/54+1/108+…+1/990=1/3.6+1/6.9+1/9.12+…+1/30.33=1/3(3/3.6+3/6.9+3/9.12+…+3/30.33)=1/3(1/3-1/6+1/6-1/9+1/9-1/12+…+1/30-1/33)=1/3(1/3-1/33)=1/3(11/33-1/33)=1/3. 10/33=10/99`

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2. `a)`

       `3/1.4 + 3/4.7 + 3/7.10 + … + 3/40.43`

   `=  1- 1/4 + 1/4 – 1/7 + 1/7 – 1/10 + … + 1/40 – 1/43`

   `= 1 – 1/43`

   `= 43/43- 1/43`

   `= 42/43`

   `b)`

   `4/2.4 + 4/4.6 + 4/6.8 +… + 2/2016.2018`

   `= 2 . ( 2/2.4 + 2/4.6 + 2/6.8 + … + 2/2016.2018)`

   `= 2 . ( 1/2 – 1/4 + 1/4 – 1/6 + 1/6 – 1/8 + … + 1/2016 – 1/2018)`

   `= 2 . (1/2 – 1/2018)`

   `= 2 . (1009/2018 – 1/2018)`

   `= 2 . 1004/1009`

   `=2008/1009`

   `c)`

   `1/18 + 1/54 + 1/108 + … + 1/990`

   `=1/3.6 + 1/6.9 + 1/9.12 + …  +1/30.33`

   `=1/3 . (1/3 – 1/6 +1/6  -1/9 +1/9 – 1/12 + … + 1/30  -1/33)`

   `=1/3 .(11/33 – 1/33)`

   `=1/3 . 10/33`

   `= 10/99`

    

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