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)` . 9873740001

Answer

N/a

Explanation

`S_(n)=(a(1-r^(n)))/(1-r)`
Sum from (n+1)th term to (2n)th term
`s_(n)=S_(2n)-S_(n)`
`=(a(1-r^(2n)))/(1-r)-(a(1-r^(n)))/(1-r)=(ar^(n)(1-r)^(n)))/(1-r)`
`Now (S_(n))/(s_(n))=((a(1-r^(n)))/(1-r))/((ar^(n)(1-r^(n)))/(1-r))`
`implies (S_(n))/(s_(n))=(1)/(r_(n))" "` Hence Proved.