数列{an}满足a1=1,an+1=an+n+1(n属于正整数) 1/a1+1/a2+.+1/a2013=an+1中(n+1)为脚标an+(n+1)中(n+1)不为脚标

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数列{an}满足a1=1,an+1=an+n+1(n属于正整数)1/a1+1/a2+.+1/a2013=an+1中(n+1)为脚标an+(n+1)中(n+1)不为脚标数列{an}满足a1=1,an+1

数列{an}满足a1=1,an+1=an+n+1(n属于正整数) 1/a1+1/a2+.+1/a2013=an+1中(n+1)为脚标an+(n+1)中(n+1)不为脚标
数列{an}满足a1=1,an+1=an+n+1(n属于正整数) 1/a1+1/a2+.+1/a2013=
an+1中(n+1)为脚标
an+(n+1)中(n+1)不为脚标

数列{an}满足a1=1,an+1=an+n+1(n属于正整数) 1/a1+1/a2+.+1/a2013=an+1中(n+1)为脚标an+(n+1)中(n+1)不为脚标
an+1=an+n+1
∴an+1-an=n+1
a2-a1=2
a3-a2=3
……
an+1-an=n+1
以上各式相加
得:-a1+an+1=2+3+4+……+n+1
=n/2(n+3)
∴an+1=n/2(n+3)+1
an=(n-1)(n+2)/2+1
1/an=2(1/n-1/n+1)
s2013=2(1-1/2+1/2-1/3+……+1/n-1/n+1)
=2(1-1/2013)
=4024/2013