cho A= 13/25+9/10-11/15+13/21-15/28+17/36-…+197/4851-199/4950. chứng minh A<9/10

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1. Đáp án + Giải thích các bước giải:

   `A=13/25+9/10-11/15+13/21-15/28+…+197/4851-199/4950`

   `A=13/25+(9/10-11/15)+(13/21-15/28)+…+(197/4851-199/4950)`

   `A=13/25+1/6+1/12+1/20+…+1/2450`

   `A=13/25+1/2.3+1/3.4+1/4.5+…+1/49.50`

   `A=13/25+1/2-1/3+1/3-1/4+1/4-1/5+…+1/49-1/50`

   `A=13/25+1/2-1/50`

   `A=26/50+25/50-1/50`

   `A=1=10/10>9/10`

   Vậy `A>9/10`

    

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2. Đáp án:

   `A>9/10`

   Giải thích các bước giải:

   `A=13/25+9/10-11/15+13/21-15/28+17/36-…+197/4851-199/4950`

   `=>A/2=13/2.25+9/2.10-11/2.15+13/2.21-15/2.28+17/2.36-…+197/2.4851-199/2.4950`

   `=>A/2=13/50+9/20-11/30+13/42-15/56+17/72-…+197/9702-199/9900`

   `=>A/2=13/50+9/4.5-11/5.6+13/6.7-15/7.8+17/8.9-…+197/98.99-199/99.100`

   `=>A/2=13/50+((1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)-…+(1/98+1/99)-(1/99+1/100))`

   `=>A/2=13/50+(1/4-1/100)`

   `=>A/2=13/50+12/50`

   `=>A/2=1/2`

   `=>A=1>9/10`

   Vậy `A>9/10`.

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