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),
∴
which is true
∴ P (m + 1) is true
∴ P(m) is trueP (m + 1) is true
Hence, by the principle of mathematical induction, P(n) is true for all