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