Question
Prove the following by using the principle of mathematical induction for all 
:
Solution
Let P(n): 
I. For n = 1,
P(1) : 
∴ P(1) is true.
II. Let the statement be true
for n = 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 the principal of mathematical induction, P(n) is true for all 
.
