证明：n=1时,由 1/2+1/3+1/4 = 13/12 = 26/24 > 25/24知不等式成立.现在设n = k的时候不等式成立,即 1/(k+1) + 1/(k+2) +...+1/(3k+1) > 25/24.①则n = k+1时,由 (3k+2)(3k+4) = (3k+3-1)(3k+3+1) = (3k+3)² - ...