Question
Use principle of mathematical induction to prove that:
Solution
Let P(n): 1 + 2 + 3 + ......... + n = 
I. For n = 1,
P(1) : 1 = 
is true.
II. Suppose the statement is true for n = m, 
i.e. P(m): 
....(i)
III. For n = m + 1,
P(m + 1): 1 + 2 + 3 + ........ + (m + 1) = 
or [1 + 2 + 3 + ...... + m] + (m + 1) = 
[From (i), 1 + 2 + 3 + ...... + m = 
]
∴ P (m + 1): 
which is true
∴ P(m + 1) is true
∴ P(m) is true 
P(m + 1) is true
Hence, by mathematical induction
P(n) is true for all 
