(1)当n≥1时,f(x)在[n,n+1]上是增函数, n=1时,f(1)=,f(2)=2×(2-)=3;有整数1,2,故g(1)=2; n=2时,f(3)=3×(3-)=,有整数4,5,6,7;故g(2)=4; n=3时,f(4)=4×(4-)=14,有整数8,9,10,11,12,13;故g(3)=6; n=4时,f(5)=5×(5-)=,有整数15,16,17,18,19,10,21,22;故g(4)=8; n=5时,f(6)=6×(6-)=33,有整数23,24,25,26,27,28,29,30,31,32;故g(5)=10; (2)∴g(n)=2n. (3)∴(Cn0+Cn1+…+Cnn)l≥g(n)-25⇒2n•L≥2n-25⇒L≥ 令an=, 则an+1-an=-=; n≤13时,an+1-an>0,{an}递增; n≥14时,an+1-an<0,{an}递减; n=13时,an有最大值,a13==. ∴L的最小值为. |