# 1 : prove : 0 = 1 - a XXXXXXXXXXan. please prove it by induction .# 2 :a) how many unbounded...

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# 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 regions formed by n different lines in the plane - No restriction. prove it by induction .

David · Accepted Answer

# 1 : prove : 0 = 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 lines in general position in the plane.

# 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...

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