Question

對(duì)于函數(shù)y=f(x)，若x₁+x₂="1," 則f(x₁)+f(x₂)=1,記數(shù)列f(),f(),
……,f()……,(n≥2，n∈)的前n項(xiàng)的和為S_{n ；}
(1)求S_n;
(2)若a=,a=" "  (n≥2，n∈),

Answer 1

 數(shù)列{a_n}的前n項(xiàng)和為T_n, 若T_n≤λ(S_n+1+1)對(duì)一切n∈都成立，試求λ的最小值.（1）S_n=(n≥2,n∈N^*).
(2)λ的最小值為

（1）由已知 x₁+x₂=1,f(x₁)+f(x₂)=1,
S_n=f( 
又 S_n=f(,
2S_n=［f()+［f()+…+［f() ="n-1"
∴S_n=(n≥2,n∈N^*).
(2)當(dāng)n≥2時(shí),a_n=
T_n=(      由T_n≤λ(S_n+1+1)得
λ≥
∵n+≥4,當(dāng)且僅當(dāng)n=2時(shí)等號(hào)成立,  ∴
故  λ的最小值為