已知数列an满足a1=2/5,且对任意n属于N*,都有an/a(n+1)=4an+2/a(n+1)+2令bn=an*an+1,Tn=b1+b2+b3.+bn求证Tn小于4|15
问题描述:
已知数列an满足a1=2/5,且对任意n属于N*,都有an/a(n+1)=4an+2/a(n+1)+2令bn=an*an+1,Tn=b1+b2+b3.+bn求证Tn小于4|15
答
a(n)/a(n+1)=[4a(n)+2]/[a(n+1)+2],[a(n+1)+2]/a(n+1)=[4a(n)+2]/a(n),2/a(n+1) + 1 = 2/a(n) + 4,2/a(n+1) = 2/a(n) + 3,{2/a(n)}是首项为2/a(1)=5, 公差为3的等差数列.2/a(n) = 5 + 3(n-1) = 3n + 2,a(n) = 2/(3n+...