# Prove the following by the principle of mathematical induction:a + ar + ar2 + … + arn – 1 Let P(n): a + ar + ar2 + … + arn - 1 = For n =1

a = a a = a

Since, P(n) is true for n = 1

Let P(n) is true for n = k , so

P(k): a + ar + ar2 + … + ark - 1 = - - - - - - - (1)

We have to show that,

a + ar + ar2 + … + ark - 1 + ark = Now,

{ a + ar + ar2 + … + ark - 1} + ark

= using equation (1)

= = = Therefore, P(n) is true for n = k + 1

Hence, P(n) is true for all n N

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