已知数列{an}中a1=1且n大于1时,2sn的平方=2ansn-an求an

问题描述:

已知数列{an}中a1=1且n大于1时,2sn的平方=2ansn-an求an

2sn^2=2ansn-an2sn^2=2[sn-s(n-1)]sn-[sn-s(n-1)]2sn^2=2sn^2-2sns(n-1)-sn+s(n-1)2sns(n-1)+sn-s(n-1)=01/sn-1/s(n-1)=2 1/sn=1/s1+2(n-1)=2n-1sn=1/(2n-1)an=sn-s(n-1)=1/(2n-1)-1/(2n-3),a1=1,an=1/(2n-1)-1/(2n-...