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a+ ar + ar^{2} + ...... + ar^{n-1}= a(r^{n}-1)/r-1 prove this by PMI .

Dear Student,

We need to prove that

........(1)

using principle of Mathematical induction.

Let *n = *1.

Plug-in this value in equation (1).

Thus,

Thus, equation (1) is true for *n = *1.

Let is true.

Then,

is true.

We need to prove that is true.

That is we need to prove that,

is true.

Consider the L.H.S of the above equation.

Since the statement is true for , we can rewrite :

Thus,

Thus, if is true then is true.

Thus, is true for all .

Regards

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