由 Tzwan 於 星期五 六月 14, 2013 1:50 pm
(f0 = 左式, g0 = 右式)
f0 = 2-1/2 + 2-5/6 > 0
g0 = 21/3 > 0
以下fx 和 gx 之間的大小關係等價於 f0 和 g0 之間的大小關係,
想法: 取平方可以讓兩數值的差距放大, 但也會讓數字更難看, 要做一些調整.
(左右式同乘22/3)
f1 = f0*22/3 = 21/6 + 2-1/6
g1 = g0*22/3 = 2
(左右式取平方)
f2 = f12 = 21/3 + 2-1/3 + 2
g2 = g12 = 4
(左右式同減2)
f3 = f2 - 2 = 21/3 + 2-1/3
g3 = g2 - 2 = 2
(左右式取平方)
f4 = f32 = 22/3 + 2-2/3 + 2
g4 = g32 = 4
(左右式同減2)
f5 = f4 - 2 = 22/3 + 2-2/3
g5 = g4 - 2 = 2
(左右式取平方)
f6 = f52 = 24/3 + 2-4/3 + 2
g6 = g52 = 4
(左右式同減2)
f7 = f6 - 2 = 24/3 + 2-4/3
g7 = g6 - 2 = 2
(左右式同乘以個別的前式)
f8 = f7 * f5 = 22 + 2-2 + 22/3 + 2-2/3
g8 = g7 * g5 = 4
(左右式同減4)
f9 = f8 - 4 = 2-2 + 22/3 + 2-2/3
g9 = g8 - 4 = 0
因 f9 > 0 = g9
所以f0 > g0