Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: a + Ar + Ar^2 + ... + Ar^(N -1) = (A(R^N - 1))/(R -1)

प्रश्न

Prove the following by using the principle of mathematical induction for all n ∈ N:

`a + ar + ar^2 + ... + ar^(n -1) = (a(r^n - 1))/(r -1)`

उत्तर

Let the given statement be P(n), i.e.,

We shall now prove that P(k + 1) is true. Consider

Thus, P(k + 1) is true whenever P(k) is true.

Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.

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Principle of Mathematical Induction

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Principle of Mathematical Induction

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