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
问题描述:
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
答
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=1-1/2a3-a2=1/2-1/3a4-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...