Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from
(n + 1) to (2n) term is 1/rn
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Answer:
ANSWER
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
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