Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from `(n+1)^(t h)`to `(2n)^(t h)`term is `1/(r^n)`

Explanation

To show that the ratio of the sum of the first \( n \) terms of a geometric progression (G.P.) to the sum of the terms from the \( (n+1)^{th} \) to the \( (2n)^{th} \) term is \( \frac{1}{r^n} \), we can follow these steps:

### Step 1: Sum of the First \( n \) Terms of a G.P.
The sum \( S_n \) of the first \( n \) terms of a G.P. with first term \( a \) and common ratio \( r \) is given by the formula:

\[ S_n = \frac{a(r^n - 1)}{r - 1} \]
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