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