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Question
Prove the following by using the principle of mathematical induction for all 
a + (a + d) + (a + 2d) + ...........+ [a + (n - 1)d] = 
Solution
Let P(n) : a + (a + d) + (a + 2d) + .............+ [a + (n - 1)d] = 
I. For n = 1,
∴ P(1) is true
II. Suppose the statement is true for n=m, 
∴ 
.... (i)
III. For n = m + 1,
or 
From (i),
∴ 
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 
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