Question

已知数列｛an｝为等差数列，公差d不等于零，an不等于零（n属于正整数）akx^2+2ak+1x+ak+2=0（1）求证

Answer 1

a(n) = a + (n-1)d,

0 = a(k)x^2 + 2a(k+1)x + a(k+2),

Delta = [2a(k+1)]^2 - 4a(k)a(k+2) = 4[a+kd]^2 - 4[a+(k-1)d][a+(k+1)d] = 4[a+kd]^2 - 4[a+kd-d][a+kd+d] = 4[a+kd]^2 -4[a+kd]^2 + 4d^2 = 4d^2>0...