Giúp tui với ạ! A= 3/1×4 + 3/4×7 + 3/7×10 +…+ 3/97×100 B= 3/1×3 +3/3×5 + 3/5×7 + …. + 3/99×101 C= 1/4 + 1/28 + 1/70 + … + 1/10300 D= 1/1×4 +1/4x

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1. `A = 3/(1 × 4) + 3/(4 × 7) + 3/(7 × 10) + … + 3/(97 × 100)`

   `A = 1 – 1/4 + 1/4 – 1/7 + 1/7 – 1/10 + … + 1/97 – 1/100`

   `A = 1 – 1/100`

   `A = 99/100`

   $\\$

   `B = 3/(1 × 3) + 3/(3 × 5) + 3/(5 × 7) + … + 3/(99 × 101)`

   `B = 3/2 × (1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + … + 1/99 – 1/101)`

   `B = 3/2 × (1 – 1/101)`

   `B = 3/2 × 100/101`

   `B = 150/101`

   $\\$

   `C = 1/(1 × 4) + 1/(4 × 7) + 1/(7 × 100) + … + 1/(52 × 55)`

   `C = 1/3 × 3 × (1/(1 × 4) + 1/(4 × 7) + 1/(7 × 100) + … + 1/(52 × 55))`

   `C = 1/3 × (3/(1 × 4) + 3/(4 × 7) + 3/(7 × 10) + … + 3/(52 × 55))`

   `C = 1/3 × (1 – 1/4 + 1/4 – 1/7 + 1/7 – 1/10 + … + 1/52 – 1/55)`

   `C = 1/3 × (1 – 1/55)`

   `C = 1/3 × 54/55`

   `C = 18/55`

   $\\$

   `F = 10 × (1/2 + 5/6 + 11/12 + 19/20 + … + 98/90)`

   `F = 10 × [(1 – 1/2) + (1 – 1/6) + (1 – 1/12) + (1 – 1/20) + … + (1 – 1/90)]`

   `F = 10 × [(1 + 1 + 1 + 1 + … + 1) – (1/2 + 1/6 + 1/12 + 1/20 + … + 1/90)]`

   `F = 10 × [9 – (1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/9 – 1/10)]`

   `F = 10 × [9 – (1 – 1/10)]`

   `F =10 × (9 – 9/10)`

   `F = 10 × 81/10`

   `F = 81`

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2. Đáp án:

    `A = 3/(1 xx 4) + 3/(4 xx 7) + …………… + 3/(97 xx 100)`

   `     = 1 – 1/4 + 1/4 – 1/7 + …………… + 1/97 – 1/100`

   `     = 1 – 1/100 = 99/100`

   `B = 3/(1 xx 3) + 3/( 3 xx 5) + ……………… + 3/( 99 xx 101)`

    `  = 3/2 xx ( 2/(1 xx 3) + 2/(3 xx 5) + …………. + 2/(99 xx 101))`

    `  = 3/2 xx ( 1 – 1/3 + 1/3 – 1/5 + ……………+ 1/99 – 1/101)`

   `   = 3/2 xx ( 1 – 1/101)`

   `   = 3/2 xx 100/101`

   `   =150/101`

   `C = 1/( 1 xx 4) + 1/(4 xx 7) + …….. + 1/(52 xx 55)`

   `   = 1/3 xx ( 3/(1 xx 4) + 3/(4 xx 7) + ………….. +3/(52 xx 55) )`

   `   = 1/3 xx ( 1 – 1/4 + 1/4 – 1/7 + ……………. + 1/52 – 1/55)`

   `   = 1/3 xx ( 1 – 1/55)`

   `    = 1/3 xx 54/55`

   `    = 18/55`

   `D = 10 xx ( 1/2 + 5/6 + 11/12 + 19/20 + ………. + 89/90)`

   `   = 10 xx ( 1 – 1/2 + 1 – 1/6 + 1 – 1/12 + ………. + 1 – 1/90)`

   `   = 10 xx [ ( 1 + 1 + 1 + ………… + 1) – (1/2 + 1/6 + 1/12 + …………… + 1/90)]`

   `   = 10 xx [  9 – ( 1/( 1 xx 2) + 1/(2 xx 3) + 1/(3 xx 4) + ……….. + 1/( 9 xx 10) ) ]`

   `   = 10 xx [ 9 – ( 1 – 1/10)]`

   `   = 10 xx [9 – 9/10]`

   `   = 10 xx 81/10`

   `   = 81`

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