`color{#CCCCFF}{M i f u y u}color{#CCCCFF}{180608}` 

Đặt `A = (1 - 1/4)(1 - 1/9)(1 - 1/16)...(1 - 1/400)`

`A = (1 - 1/2^2)(1 - 1/3^2)(1 - 1/4^2)...(1 - 1/20^2)`

`A = ((2^2-1)/2^2)((3^2-1)/3^2)((4^2-1)/4^2)...((20^2-1)/20^2)`

`A = ((2-1)(2+1))/(2*2)*((3-1)(3+1))/(3*3)*... *((20-1)(20+1))/(20*20)`

`A = (1*2*3*...*19)/(2*3*4*...*20) * (3*4*5*...*21)/(2*3*4*...*20)`

`A = 1/20 * 21/2`

`A = 21/40`

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Đặt `A = (1 - 1/(1+2))(1 - 1/(1+2+3))...(1 - 1/(1+2+3+...+n))`

`A = ((2-1)(2+2))/(2(2+1)) * ((3-1)(3+2))/(3(3+1)) * ((4-1)(4+2))/(4(4+1)) * ... * ((n-1)(n+2))/(n(n+1))`

`A = (1*4)/(2*3) * (2*5)/(3*4) * (3*6)/(4*5) * ... * ((n-1)(n+2))/(n(n+1))`

`A = (1*2*3*...*(n-1))/(2*3*4*...*n) * (4*5*6*...*(n+2))/(3*4*5*...*(n+1))`

`A = (n-1)/n * (n+2)/(3(n+1))`

`A = ((n-1)(n+2))/(3n + 1)`

`A = (n^2 + 2n - n - 2)/(3n + 1)`

`A = (n^2 + n - 2)/(3n+1 )`