Show that in an infinite G.P. with common ratio `r(|r|<1)` , each term bears a constant ratio to the sum of all terms that follow it.

Explanation

Let take `a, ar, ar^2, ar^3,.....`


We know, general term `ar^(n-1) . . . (1)`


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

`=(ar^n)/(1-r)`` \ \ \ \ (2)`

Divide eq `(1)` by eq `(2)`

`= (ar^(n-1))/((ar^n)/(1-r))`

`= ((1-r)(ar^(n-1)))/(ar^n)`

`=(1-r)/r`

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