1若a0=b0=1,an=an-1+2bn-1,bn=an-1+bn-1则a1^2-2b1^2=?,a2^2-2b2^2=?,a3^2-2b3^2=?a2005^2-b2005^2=?2设正数数列{an}的前n项和为Sn,且存在正数t,使得对所有正整数n都有√(tSn)=(t+an)/2,则Sn=?

Question

1若a0=b0=1,an=an-1+2bn-1,bn=an-1+bn-1则 a1^2-2b1^2=?,a2^2-2b2^2=?,a3^2-2b3^2=?a2005^2-b2005^2=?
2设正数数列{an}的前n项和为Sn,且存在正数t,使得对所有正整数n都有√(tSn)=(t+an)/2,则Sn=?

Answer 1

(1)若a0=b0=1,an=an-1+2bn-1,bn=an-1+bn-1a1=a0+2b0=3,b1=a0+b0=2,a1²-2b1²=3²-2*2²=1；a2=a1+2b1=7,b2=a1+b1=5,a2²-2b2²=7²-2*5²=-1；a3=a2+2b2=17,b3=a2+b2=12,a2²-...