Mathematical Induction


   
 
Principle of Mathematical Induction (PMI)
 
(i) P(1) is true
 
(ii) P(r) is true P(r+1) is true.
 
Algorithm for proving a statement by P.M.I
 
Step I: Denote the statement involving natural numbers n = 1, 2,…. by P(n).
 
Step II: Prove that the statement P(1) holds good by putting n = 1 on one side of the statement and then simplifying it to take the form of the expression on the other side.
 
Step III: Assume that the statement p(n) is true for n = r, i.e., P(r) is true.
 
Step IV: Use the assumption p(r) is true, to prove p(r+1) is true.
 
 
 
     
   
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