1/1×2×3+1/2×3×4+1/3×4×5+.1/20×21×22解答都是分数
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![1/1×2×3+1/2×3×4+1/3×4×5+.1/20×21×22解答都是分数](/uploads/image/z/5936138-26-8.jpg?t=1%2F1%C3%972%C3%973%2B1%2F2%C3%973%C3%974%2B1%2F3%C3%974%C3%975%2B.1%2F20%C3%9721%C3%9722%E8%A7%A3%E7%AD%94%E9%83%BD%E6%98%AF%E5%88%86%E6%95%B0)
1/1×2×3+1/2×3×4+1/3×4×5+.1/20×21×22解答都是分数
1/1×2×3+1/2×3×4+1/3×4×5+.1/20×21×22解答
都是分数
1/1×2×3+1/2×3×4+1/3×4×5+.1/20×21×22解答都是分数
由于1/n(n+1)(n+2) = ( 1/n(n+1) - 1/(n+1)(n+2) ) / 2
代入上面的式子得到
原式 = 1/2( 1/1*2 - 1/2*3 + 1/2*3 - .-1/21*22)
= 1/2( 1/2 - 1/21*22 )
= 115/462