数列｛an｝中,满足a1=1,an+1=an+n,求｛an｝.不懂得不要乱说

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数列｛an｝中,满足a1=1,an+1=an+n,求｛an｝.不懂得不要乱说
数列｛an｝中,满足a1=1,an+1=an+n,求｛an｝.不懂得不要乱说

数列｛an｝中,满足a1=1,an+1=an+n,求｛an｝.不懂得不要乱说
A1=1
An+1-An=n
则A2-A1=1
A3-A2=2
A4-A3=3
.
An-An-1=n-1
An+1-An=n
全部相加得：An+1-A1=(1+n)n/2
An+1=(1+n)n/2+1
An=(1+n-1)(n-1)/2+1
An=n(n-1)/2+1

简单，a2-a1=0 a3-a2=1......相加
an-a1=(n-1)*n/2
an=1+(n-1)*n/2
当n=1时成立

a2-a1=0 a3-a2=1......相加
an-a1=(n-1)*n/2(不包括n=1)
当n=1时
an=1+(n-1)*n/2
=1=a1
所以
an=1+(n-1)*n/2

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