Question

Show that the ratio of the sum of first n terms of a GP to the sum of terms from
(n + 1) to (2n) term is 1/rⁿ​

Answer 1

S

n

=

1−r

a(1−r

n

)

Sum from (n+1)th to 2nth terms is =S

2n

−S

n

=

1−r

a(1−r

2n

)

−

1−r

a(1−r

n

)

=

1−r

a

(r

n

−r

2n

)

Ratio is given by,

=

1−r

a

(r

n

−r

2n

)

1−r

a(1−r

n

)

=

1−r

a

r

n

(1−r

n

)

1−r

a(1−r

n

)

=

r

n

1

Ans