`1)`

`A = 4/(3*6) + 4/(6*9) + ... + 4/(96*99)`

`A = 4/3 * ( 3/(3*6) + 3/(6*9) + ... + 3/(96*99) )`

`A = 4/3 * ( 1/3 - 1/6 + 1/6 - 1/9 + ... + 1/96 - 1/99 )`

`A = 4/3 * ( 1/3 - 1/99 )`

`A = 4/3 *  32/99`

`A = 128/297`

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`2)`

`B = (1 - 1/2^2) * (1 - 1/3^2) * ... * (1 - 1/10^2)`

`B = 3/4 * 8/9 * ... * 99/100`

`B = (1*2*...*9)/(2*3*...*10) * (3*4*...*11)/(2*3*...*10)`

`B = 1/10 * 11/2`

`B = 11/20` *

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`3)`

`C = (1/10 - 1) * (1/11 - 1) * ... * (1/100 - 1)`

`C = (-9/10) * (-10/11) * ... * (-99/100)`

Số thừa số là:

`100 - 10 + 1 = 91` (thừa số)

`=> C = - (9/10 * 10/11 * ... * 99/100)`

`=> C = -9/100` 

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`4)`

`S = 1/3 + 1/3^2 + ... + 1/3^300`

`3S = 1 + 1/3 + 1/3^2 + ... + 1/3^299`

`3S - S = (1 + 1/3 + ... + 1/3^299) - (1/3 + 1/3^2 + ... + 1/3^300)`

`2S = 1 - 1/3^300`

`S = (1 - 1/3^300) / 2`

`S = (3^300 - 1) / (2 * 3^300)`