### Re: [問題]求x的值

tangpakchiu 寫到:#ed_op#div#ed_cl##ed_op#img alt="image file name: 2k40f1d85540.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2k40f1d85540.gif" border="0"#ed_cl##ed_op#/div#ed_cl##ed_op#div#ed_cl#&nbsp;#ed_op#/div#ed_cl##ed_op#div#ed_cl#大家幫幫忙吧~~~#ed_op#/div#ed_cl#
#ed_op#br#ed_cl#簡單快速的方法：#ed_op#br#ed_cl#(1+1/2003)#ed_op#sup#ed_cl#2003#ed_op#/sup#ed_cl# = (2004/2003)#ed_op#sup#ed_cl#2003#ed_op#/sup#ed_cl# = (2003/2004)#ed_op#sup#ed_cl#-2003#ed_op#/sup#ed_cl# = [(2004-1)/2004]#ed_op#sup#ed_cl#-2004+1#ed_op#/sup#ed_cl# =&nbsp; (1-1/2004)#ed_op#sup#ed_cl#-2004+1#ed_op#/sup#ed_cl# = (1+1/-2004)#ed_op#sup#ed_cl#-2004+1#ed_op#/sup#ed_cl#  =&gt; x = -2004#ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#br#ed_cl#x明顯不會是正整數，因為∀x&gt;0, (1+1/x)#ed_op#sup#ed_cl#x+1#ed_op#/sup#ed_cl# dec,&nbsp; lim(1+1/x)#ed_op#sup#ed_cl#x+1#ed_op#/sup#ed_cl# = e; (1+1/x)#ed_op#sup#ed_cl#x+1#ed_op#/sup#ed_cl#&nbsp; &gt; e #ed_op#span style="font-weight: bold;"#ed_cl#&gt;#ed_op#/span#ed_cl# (1+1/2003)#ed_op#sup#ed_cl#2003#ed_op#/sup#ed_cl# ，故x必為負數。#ed_op#br#ed_cl#設 y=-x =&gt; (1+1/-y)#ed_op#sup#ed_cl#-y+1#ed_op#/sup#ed_cl# = (1-1/y)#ed_op#sup#ed_cl#1-y#ed_op#/sup#ed_cl# = [(y-1)/y]#ed_op#sup#ed_cl#1-y#ed_op#/sup#ed_cl# = [y/(y-1)]#ed_op#sup#ed_cl#y-1#ed_op#/sup#ed_cl# = [(y-1+1)/(y-1)]#ed_op#sup#ed_cl#y-1#ed_op#/sup#ed_cl# = [1+1/(y-1)]#ed_op#sup#ed_cl#y-1#ed_op#/sup#ed_cl# =&gt; y-1=2003 =&gt; y=2004 =&gt; x=-2004#ed_op#br#ed_cl#

### [問題]求x的值

#ed_op#DIV#ed_cl##ed_op#IMG alt="image file name: 2k40f1d85540.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2k40f1d85540.gif" border=0#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#大家幫幫忙吧~~~#ed_op#/DIV#ed_cl#