Long Answer TypeProve the following by using the principle of mathematical induction for all 
a + (a + d) + (a + 2d) + ...........+ [a + (n - 1)d] = 
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. Â Â 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 
        Â
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