Question
Prove the following by using the principle of mathematical induction for all 
:
Solution
Let P(n) : 
I. For n = 1,
P(1) : 1 
∴ P(1) is true.
II. Let the statement be true for n = m, 
∴ P(m) : 
... (i)
III. For n = m + 1,
P(m + 1) : 
or 
From (i), 
∴ 
which is true.
∴ P(m + 1) is true.
∴ P(m) is true 
P (m + 1) is true
Hence, by principle of mathematical induction, P(n) is true for all 
