Principle of Mathematical Induction PPT Maths Class 11

 Page 3


?In algebra or in other discipline of 
mathematics, there are certain results or 
statements that are formulated in terms 
of n, where n is a positive integer. To 
prove such statements well-suited 
principle that is used-based on the 
specific technique is know as the 
principle of mathematical induction.
Page 4


?In algebra or in other discipline of 
mathematics, there are certain results or 
statements that are formulated in terms 
of n, where n is a positive integer. To 
prove such statements well-suited 
principle that is used-based on the 
specific technique is know as the 
principle of mathematical induction.
? The principle of mathematical induction is 
one such tool which can be used to prove a 
wide variety of mathematical statements. 
Each such statement is assumed as P(n) 
associated with positive integer n, for which 
the correctness for the case n=1 is examined. 
Then assuming the truth of P(k) for some 
positive integer k, the truth of P(k+1) is 
established. 
Page 5


?In algebra or in other discipline of 
mathematics, there are certain results or 
statements that are formulated in terms 
of n, where n is a positive integer. To 
prove such statements well-suited 
principle that is used-based on the 
specific technique is know as the 
principle of mathematical induction.
? The principle of mathematical induction is 
one such tool which can be used to prove a 
wide variety of mathematical statements. 
Each such statement is assumed as P(n) 
associated with positive integer n, for which 
the correctness for the case n=1 is examined. 
Then assuming the truth of P(k) for some 
positive integer k, the truth of P(k+1) is 
established. 
? There is a given statement P(n) involving the 
natural number n such that
(i) The statement is true for n=1, i.e., P(1) is 
true, and
(ii) If the statement is true for n=k (where k is 
some positive integer ), then the statement  
is also true for n=k+1 , i.e., truth of P(k) 
implies the truth  of P(k+1).
(iii) Then, P(n) is true for all natural numbers 
n.