计算出a1=1,a2=根号2-1,a3=根号3-2猜想an=根号n-根号(n-1),Sn=根号n用数学归纳法证明n=1时2a1=a1+1/a1,a1=1成立假设n=k成立,则n=k+1时2√k+2a(k+1)=a(k+1)+1/a(k+1)整理得[a(k+1)+√k]^2=k+1所以a(k+1)=√(k+1)-√k...