已知数列{an}满足an+1=an+n,a1=1,则an=______.-数学

题目简介

已知数列{an}满足an+1=an+n,a1=1,则an=______.-数学

题目详情

已知数列{an}满足an+1=an+n,a1=1,则an=______.
题型:填空题难度:中档来源:不详

答案

∵an+1=an+n,a1=1,
∴a2-a1=1
a3-a2=2

an-an-1=n-1
以上n-1个式子相加可得,an-a1=1+2+…+n-1=class="stub"1+n-1
2
×(n-1)
=
n2-n
2

an=class="stub"1
2
n2-class="stub"1
2
n+1

故答案为:an=class="stub"1
2
n2-class="stub"1
2
n+1

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