baì 4 a) a= 1/5+1/20+1/44+1/77+..+1/5252 b= 2/3+14/15+34/35+62/63+98/99

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1. Đáp án:

    

   Giải thích các bước giải:

   `A=1/5+1/20+1/44+1/77+…+1/5252`

   `=>A/2=1/10+1/40+1/88+1/154+…+1/10504`

   `=>A/2=1/2.5+1/5.8+1/8.11+1/11.14+…+1/101.104`

   `=>(3A)/2=3/2.5+3/5.8+3/8.11+3/11.14+…+3/101.104`

   `=>(3A)/2=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+…+1/101-1/104`

   `=>(3A)/2=1/2-1/104`

   `=>(3A)/2=51/104`

   `=>3A=51/104*2`

   `=>3A=51/52`

   `=>A=51/52÷3`

   `=>A=51/156`

   Vậy `A=51/156`.

   `B=2/3+14/15+34/35+62/63+98/99`

   `=>B=(1-1/3)+(1-1/15)+(1-1/35)+(1-1/63)+(1-1/99)`

   `=>B=5-(1/3+1/15+1/35+1/63+1/99)`

   `=>B=5-(1/1.3+1/3.5+1/5.7+1/7.9+1/9.11)`

   `=>B=5-1/2(2/1.3+2/3.5+2/5.7+2/7.9+2/9.11)`

   `=>B=5-1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)`

   `=>B=5-1/2(1-1/11)`

   `=>B=5-1/2*10/11`

   `=>B=5-5/11`

   `=>B=50/11`

   Vậy `B=50/11`.

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2. $\text{Bài 4:}$

   `a, A = 1/5 + 1/20 + 1/44 + 1/77 + …+ 1/5252`

   `⇒ A = 2/10 + 2/40 + 2/88 + 2/154 + … + 2/10504`

   `⇒ A = 2/2.5 + 2/5.8 + 2/8.11 + 2/11.14 +…+ 2/101.104`

   `⇒ A = 2/3 . (3/2.5 + 3/5.8 + 3/8.11 + 3/11.14 +…+ 3/101.104)`

   `⇒ A = 2/3 . (1/2 – 1/5 + 1/5 – 1/8 +…+ 1/101 – 1/104)`

   `⇒ A = 2/3 . (1/2 – 1/104)`

   `⇒ A = 1/3 – 1/156`

   `⇒ A = 52/156 – 1/156 = 51/156`

   `b, B =  2/3 + 14/15 + 34/35 + 62/63 + 98/99`

   `⇒ B = (1 – 1/3) + (1 – 1/15) + (1 – 1/35) + (1 – 1/63) + (1 – 1/99)`

   `⇒ B = (1 + 1 + 1 + 1 + 1) – (1/3 + 1/15 + 1/35 + 1/63 + 1/99)`

   `⇒ B = 5 – (1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11)`

   `⇒ B = 5 – 1/2 . (2/1.3 + 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11)`

   `⇒ B = 5 – 1/2 . (1 – 1/3 + 1/3 – 1/5 + … + 1/9 – 1/11)`

   `⇒ B = 5 – 1/2 . (1 – 1/11)`

   `⇒ B = 5 – 1/2 . 10/11`

   `⇒ B = 5 – 5/11 = 50/11` 

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