Prove the following by using the principle of mathematical induction for all .
Let
I. For n = 2(note this step, n>1)
which is true
∴ P(n) is true for n = 2
II. Suppose the statement is true for n = m,
.... (i)
III. For n = m + 1,
or
or
Adding on both sides of (i), we get
But,
∴
∴ P (m + 1) is true
∴ P(m) is true P(m + 1) is true
Hence, P(n) is true for all