已知数列 {an}中,a1=1,sn为其前n项和,当n≥2时,an=(√ ̄sn+√ ̄sn-1)⼀2.证明数列{√ ̄sn}是等差数列

2025-05-21 07:26:35
推荐回答(1个)
回答1:

An=Sn-S(n-1)=[(Sn)^0.5+(S(n-1))^0.5]×[(Sn)^0.5-(S(n-1))^0.5]
2An=[(Sn)^0.5+(S(n-1))^0.5]
两式相除
[(Sn)^0.5-(S(n-1))^0.5]=0.5
{(Sn)^0.5}是等差数列