tangpakchiu 寫到:
大家幫幫忙吧~~~
簡單快速的方法:
(1+1/2003)
2003 = (2004/2003)
2003 = (2003/2004)
-2003 = [(2004-1)/2004]
-2004+1 = (1-1/2004)
-2004+1 = (1+1/-2004)
-2004+1 => x = -2004
x明顯不會是正整數,因為∀x>0, (1+1/x)
x+1 dec, lim(1+1/x)
x+1 = e; (1+1/x)
x+1 > e
> (1+1/2003)
2003 ,故x必為負數。
設 y=-x => (1+1/-y)
-y+1 = (1-1/y)
1-y = [(y-1)/y]
1-y = [y/(y-1)]
y-1 = [(y-1+1)/(y-1)]
y-1 = [1+1/(y-1)]
y-1 => y-1=2003 => y=2004 => x=-2004