计算:1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)并求当n=1时代数式的值

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计算:1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)并求当n=1时代数式的值

计算:1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)并求当n=1时代数式的值
计算:1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)
并求当n=1时代数式的值

计算:1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)并求当n=1时代数式的值
答:
1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+.+1/(n+2012)-1/(n+2013)
=1/n-1/(n+2013)
=2013/[n(n+2013)]
n=1时,原式=2013/2014

1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+***+1/(n+2012)-1/(n+2013)
=1/n-1/(n+2013)
=2013/(n*(n+2013))

当n=1时
1/n(n+1)+1/(n+1)(n+2)+***+1/(n+2012)(n+2013)
=2013/(n*(n+2013))
=2013/2014