数列{an}满足a1=1,a(n+1)=an+n+1(n∈N*),则1/a1 +1/a2 +...+1/a2013=

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数列{an}满足a1=1,a(n+1)=an+n+1(n∈N*),则1/a1+1/a2+...+1/a2013=数列{an}满足a1=1,a(n+1)=an+n+1(n∈N*),则1/a1+1/a2+

数列{an}满足a1=1,a(n+1)=an+n+1(n∈N*),则1/a1 +1/a2 +...+1/a2013=
数列{an}满足a1=1,a(n+1)=an+n+1(n∈N*),则1/a1 +1/a2 +...+1/a2013=

数列{an}满足a1=1,a(n+1)=an+n+1(n∈N*),则1/a1 +1/a2 +...+1/a2013=
a1=1
a2-a1=2
a3-a2=3
.
.
an-a(n-1)=n
an=1+2+3+.+n=n(n+1)/2
1/an=2[1/n-1/(n+1)]
1/a1+...+1/a2013=2[(1-1/2)+(1/2-1/3)+.+(1/2013-1/2014)]=4026/2014

差后等差的典型，自己算吧！不难。

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