已知数列{an},a1=1,当n大于等于2时,an=[根号下sn+根号下s(n-1)]/2.

sn-s(n-1)=an=[√sn+√s(n-1)]/2√sn-√s(n-1)=1/2√sn-√s1=(n-1)/2√sn=(n+1)/2√sn为等差数列sn=(n+1)(n+1)/4an=sn-s(n-1)=(n+1)(n+1)/4-n*n/4=(2n+1)/4 (n>=2)n=1时 an=1n>1时 an=(2n+1)/4