已知数列{an}满足a1=1/2,a1+a2+.+an=n^2an,用数学归纳法证明:an=1/n(n+1)

问题描述:

已知数列{an}满足a1=1/2,a1+a2+.+an=n^2an,用数学归纳法证明:an=1/n(n+1)

1、n=1是a1=1/2满足n=2时a2+a1=4a2得a2=1/3满足2、设n=k时ak=1/k(k+1)=1/k-1/(k+1)n=k+1时a1+a2+a3……+ak+ak+1=(k+1)^2*ak+11/1-1/2+1/2-1/3……+1/k-1/(k+1)=k(k+2)ak+11-1/k+1=k(k+2)ak+1所以ak+1=1/...