已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an

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已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an

已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an
已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an
已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an

已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an已知数列{a}满足a1=1/2,a(n+1)=an+1/(n^2+n),求an
a(n+1)=an+1/(n^2+n)
a(n+1)-an=1/[n(n+1)]
a(n+1)-an=1/n-1/(n+1)
所以
a2-a1=1-1/2
a3-a2=1/2-1/3
a4-a3=1/3-1/4
.
an-a(n-1)=1/(n-1)-1/n
以上式子左右分别累加得到
an-a1=1-1/n
所以an=a1+1-1/n=1/2+1-1/n=3/2-1/n