Principle of Mathematical Induction Class 11 Notes Chemistry Chapter 4

 Page 1


 
KEY POINTS
? A meaningful sentence which can be judged to be either true or 
false is called a statement. 
? A statement involving mathematical relations is called as 
mathematical statement. 
? Induction and deduction are two basic processes of reasoning. 
? Deduction is the application of a general case to a particular 
case. In contrast to deduction, induction is process of reasoning 
from particular to general. 
? Induction being with observations. From observations we arrive 
at tentative conclusions called conjectures. The process of 
induction help in proving the conjectures which may be true. 
? Statements like(i) 
( 1)
1 2 3 .........
2
n n
n
?
? ? ? ? ?
? n ? N. 
(ii) 2 2
n
? ? n ? N. 
(iii) If n(A)=n then number of all subsets of 2
n
A ? ? n ? N. 
Page 2


 
KEY POINTS
? A meaningful sentence which can be judged to be either true or 
false is called a statement. 
? A statement involving mathematical relations is called as 
mathematical statement. 
? Induction and deduction are two basic processes of reasoning. 
? Deduction is the application of a general case to a particular 
case. In contrast to deduction, induction is process of reasoning 
from particular to general. 
? Induction being with observations. From observations we arrive 
at tentative conclusions called conjectures. The process of 
induction help in proving the conjectures which may be true. 
? Statements like(i) 
( 1)
1 2 3 .........
2
n n
n
?
? ? ? ? ?
? n ? N. 
(ii) 2 2
n
? ? n ? N. 
(iii) If n(A)=n then number of all subsets of 2
n
A ? ? n ? N. 
 
(iv) 
2( 1 )
1
n
r
Sn
r
?
?
?
 where Sn is sum of n terms of G.P,  a = 1
st
term and r = common ratio. Are all concerned with n ? N which 
takes values 1,2, 3,…. Such statements are denoted by P(n). By 
giving particular values ton, we get particular statement as P(1), 
P(2),…….. P(k) for some k ?N. 
Principle of mathematical Induction: 
Let P(n) be any statement involving natural number n such that 
(i) P(1) is true, and 
(ii) If P(k) is true ?P(k+1) is true for some some k ?N. that is 
P(KH) is true whenever P(K) is true for some k ?N then 
P(n) is true ? n ? N.