# 1 : prove : 0 = 1 - a XXXXXXXXXXan. please prove it by induction . # 2 : a) how many unbounded regions are formed by n lines in general position in the plane. b): what is the minimum number of...

# 1 : prove : 0 < a i < 1 , i = 1 , 2 , ...... m. ( 1 - a1 ) .........( 1 - an ) >= 1 - a1 - ....... - an. please
prove it by induction .
Sol:
For n=1,
For n=2,
( )( )
Let the given expression is true for n terms,
( )( ) ( )
For n+1 terms,
( )( ) ( )( )
( )( ) ( ) ( )( ) ( )
( )( ) ( )
Since ,
( )( ) ( )
( )( ) ( )
Hence,
( )( ) ( ) ( )( ) ( )

Hence, for any natural number n,
( )( ) ( )
# 2:
a. How many unbounded regions are formed by n...