1、條件：2*S(2)=S(3)+S(4)即2*( a(1)+a(2) )=2*( a(1)+a(2)+a(3) ) +a(4),所以a(4)= -2*a(3)
q=-2
2、a(n) = a(1)*q^(n-1) = (-2)^(n+1)
3、b(n) = log2|a(n)| = log2[ 2 ^(n+1) ] = n+1
4、1 / [ b(n) * b(n+1) ] = 1 / [ (n+1)*(n+2) ] = 1/ (n+1) - 1/ (n+2)
T(n) = [ 1/2- 1/3] + [ 1/3 - 1/4 ] +.+ [ 1/ (n+1) - 1/ (n+2) ] = 1/2 -1/(n+2)
5、λ》T(n)/b(n+1) =n / [ 2*(n+2)^2 ] = 1/2 * 1/[ (n+4/n) + 4]
因?yàn)閚+4/n 最小只能取到4,所以1/2 * 1/[ (n+4/n) + 4]最大取到 1/16
所以 λ最小值為1/16