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a1=1/1*2*3+1/2=2/3;a2=1/2*3*4+1/3=3/8,a3=1/3*4*5+1/4=4/15``````依据上述规律,a99=.100/9999
题目详情
a1=1/1*2*3+1/2=2/3; a2=1/2*3*4+1/3=3/8,a3=1/3*4*5+1/4=4/15``````依据上述规律,a99=____.100/9999
▼优质解答
答案和解析
an=1/[n*(n+1)*(n+2)]+1/(n+1)
通分得[1+n*(n+2)]/[n*(n+1)*(n+2)]
=[(n+1)*(n+1)]/[n*(n+1)*(n+2)]
=(n+1)/[n*(n+2)]
a99=100/(99*101)=100/9999
通分得[1+n*(n+2)]/[n*(n+1)*(n+2)]
=[(n+1)*(n+1)]/[n*(n+1)*(n+2)]
=(n+1)/[n*(n+2)]
a99=100/(99*101)=100/9999
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