原式=1-1/2+1/2-1/3……
即1/(n*(n+1))=1/n-1/(n+1)
所以原式=1-1/5=4/5.
1/1*2+1/2*3+1/3*4+1/4*5
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/2+1/2+1/3-1/3+1/4-1/4-1/5
=1-1/5
=4/5
1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
1/4*5=1/4-1/5
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/2+1/2+1/3-1/3+1/4-1/4-1/5
=1-1/5
=4/5
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5=1-1/5=4/5
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