2乘3分之一加3乘4分之一加4乘
因为1/[n*(n+1)]=(1/n)-[1/(n+1)]
所以:
1/(2*3)+1/(3*4)+1/(4*5)+……+1/(49*50)
=[(1/2)-(1/3)]+[(1/3)-(1/4)]+……+[(1/49)-(1/50)]
=(1/2)-(1/50)
=(25-1)/50
=24/50
=12/25。
因为1/[n*(n+1)]=(1/n)-[1/(n+1)]
所以:
1/(2*3)+1/(3*4)+1/(4*5)+……+1/(49*50)
=[(1/2)-(1/3)]+[(1/3)-(1/4)]+……+[(1/49)-(1/50)]
=(1/2)-(1/50)
=(25-1)/50
=24/50
=12/25。
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