An infinite ladder network of resistances is constructed with \( 1 \mathrm{ohm} \) and \( 2 \mat...

An infinite ladder network of resistances is constructed with \( 1 \mathrm{ohm} \) and \( 2 \mathrm{ohm} \) resistances Fig. The 6 Vbattery between \( A \) and \( B \) has negligible internal resistance.
Show that effective resistance between \( A \) and \( B \) is \( 2 \mathrm{ohm} \).
 
What is the current that passes through \( 2 \Omega \) resistance nearest to the battery?