Question

这道数列难题怎么做啊 求大神

Answer 1

a2=√3，s2=1+√3.
a3=√[4+2√3+2+√3]=(1+√3)√6/2，s3=(1+√3)(1+√6/2),
a4=√[(4+2√3)(5/2+√6)+(1+√3)(1+√6/2）+1]
=√[10+5√3+4√6+6√2+1+√3+√6/2+3√2/2+1]
=√[12+6√3+9√6/2+15√2/2],繁！

a<n+1>=√(sn^2+sn+1),
n>1时an=√[s<n-1>^2+s<n-1>+1],
∴[a<n+1>+an][a<n+1>-an]=sn^2-s<n-1>^2+sn-s<n-1>
=an[sn+s<n-1>+1]=an[2sn+1-an],
∴a<n+1>^2=an(2sn+1),
∴a<n+1>^2/an=2sn+1,繁！