CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 4 – Principle of Mathematical Induction Maths
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k1 k11
Thus,
2 2
4
2
k1 k11
2
P k 1
is true whenever
Pk
is true.
Hence, by the principle of mathematical induction, statement
numbers i.e., N.
Pn
is true for all natural
Question 3:
Prove the following by using the principle of mathematical induction for all
1 1 1 2n
1 .....
1 2 1 2 3 1 2 3 ... n n1
Solution 3:
Let the given statement be
P n
For
,
P n
i.e.,
1 1 1 2n
:1 .....
1 2 1 2 3 1 2 3 .... n n1
n 1, we have
2.1 2
P 1 :1 1,
11 2
Let
Pk
which is true.
be true for some positive integer k, i.e.,
1 1 1 2k
1 ... .... ....... i
1 2 1 2 3 1 2 3 ..... k k1
We shall now prove that Pk 1
is true.
Consider
1 1 1 1
1 .....
1 2 1 2 3 1 2 3 ..... k 1 2 3 ..... k k 1
1 1 1
1
1 ....
1 2 1 2 3 1 2 3 ..... k 1 2 3 .... k k 1
2k
1
k 1 1 2 3 ..... k k 1
[Using (i)]
n
N: