Question

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

Answer 1

Answer:

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Step-by-step explanation:

Sum of first n terms,

S

n

=

1−r

a(1−r

n

)

Sum of terms from (n+1)th to 2n th term 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,

=

1−r

a(r

n

−r

2n

)

1−r

a(1−r

n

)

=

r

n

−r

2n

1−r

n

=

r

n

(1−r

n

)

1−r

n

=

r

n

1