2个回答
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1/n(n+1)(n+2)=[1/n-1/(n+1)]-[1/(n+1)-1/(n+2)]
2/1*2*3+2/2*3*4+2/3*4*5+....2/*8*9*10
=2*(1/1*2*3+1/2*3*4+...+1/8*9*10)
=2*[(1-1/2+1/2-1/3+...+1/8-1/9)-(1/2-1/3+1/3-1/4+...+1/9-1/10)]
=2*[(1-1/9)-(1/2-1/10)]
=2*(8/9-2/5)
=44/45
2/1*2*3+2/2*3*4+2/3*4*5+....2/*8*9*10
=2*(1/1*2*3+1/2*3*4+...+1/8*9*10)
=2*[(1-1/2+1/2-1/3+...+1/8-1/9)-(1/2-1/3+1/3-1/4+...+1/9-1/10)]
=2*[(1-1/9)-(1/2-1/10)]
=2*(8/9-2/5)
=44/45
展开全部
答:1/n(n+1)(n+2)=[1/n-1/(n+1)]-[1/(n+1)-1/(n+2)]
2/1*2*3+2/2*3*4+2/3*4*5+....2/*8*9*10
=2*(1/1*2*3+1/2*3*4+...+1/8*9*10)
=2*[(1-1/2+1/2-1/3+...+1/8-1/9)-(1/2-1/3+1/3-1/4+...+1/9-1/10)]
=2*[(1-1/9)-(1/2-1/10)]
=2*(8/9-2/5)
=44/45
2/1*2*3+2/2*3*4+2/3*4*5+....2/*8*9*10
=2*(1/1*2*3+1/2*3*4+...+1/8*9*10)
=2*[(1-1/2+1/2-1/3+...+1/8-1/9)-(1/2-1/3+1/3-1/4+...+1/9-1/10)]
=2*[(1-1/9)-(1/2-1/10)]
=2*(8/9-2/5)
=44/45
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