Cho `G = (1-1/3)(1-1/6)(1-1/10)(1-1/15) x^(m+1) y^(m+2) z^(m+3)`
`H=(1-1/21)(1-1/28)(1-1/36)(1-1/45) x^(n-1) y^(n-2) z^(m-3)`
Với m,n ∈N; n ≥2 ; m ≥ 3
Tính G . H
Cho `G = (1-1/3)(1-1/6)(1-1/10)(1-1/15) x^(m+1) y^(m+2) z^(m+3)` `H=(1-1/21)(1-1/28)(1-1/36)(1-1/45) x^(n-1) y^(n-2) z^(m-3)` Với m,n ∈N; n ≥2
By Brielle
`G.H = (1-1/3) ( 1-1/6)(1-1/10)(1-1/15) x^(m+1) . y^(m+2) . z^(m+3) . (1-1/21) ( 1-1/28)( 1-1/36)( 1-1/45). x^(n-1). y^(n-2) . z^(m-3)`
`G.H = (1-1/3)(1-1/6)(1-1/10)(1-1/15)(1-1/21)(1-1/28)(1-1/36)(1-1/45).x^(m+1) . y^(m+2) . z^(m+3) . x^(n-1). y^(n-2) . z^(m-3)`
Đặt `A= (1-1/3)(1-1/6)(1-1/10)(1-1/15)(1-1/21)(1-1/28)(1-1/36)(1-1/45)`
`A= ( 1-2/2.3) ( 1- 2/3.4) ( 1- 2/4.5)( 1- 2/5.6) ( 1- 2/6.7)(1- 2/7.8)(1- 2/8.9)( 1-2/9.10)`
`A= 4/6 . 10/12 . 18/20 . 28/30 . 40/42 . 54/56 . 70/72 . 88/90`
`A= 1.4/2.3 . 2.5/3.4 . 3.6/4.5 . 4.7/5.6 . 5.8/6.7 . 6.9/7.8 . 7.10/8.9 . 8.11/9.10`
`A= (1.2.3….8)/(2.3.4….9) . (4.5.6…11)/(3.4.5….10)`
`A= 1/9 . 11/3`
`A= 11/27`
`=> G.H = 11/27 . x^(m+1) . y^(m+2) . z^(m+3) . x^(n-1) . y^(n-2) . z^(m-3)`
`=> G.H= 11/27 . x^(m+1 + n-1) . y^(m+2 + n-2) . z^(m+3 + m-3)`
`=> G.H=11/27 . x^(m+n) . y^(m+n) . z^(2m)`
`=> G.H= 11/27 . (xy)^(m+n) . z^(2m)`
Vậy `G.H= 11/27 . (xy)^(m+n) . z^(2m)`