Abstract: The relationship of recursion is used to deduce the equivalent resistance of ladder-shaped resistance network,and it is proved that when in certain condition of series,the equivalent resistance can reach a certain value with some error range.Meanwhile,this analysis method of working out ladder-shaped resistance network's voltage of joint through recursion relationship can be used in complex circuit network and analysis of algorithm practically.

Key words: ladder-shaped network, equivalent resistance, mother function, voltage of joint, the relationship of recursion