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Byju's Answer
Standard XII
Mathematics
Sum of n Terms
If the sum an...
Question
If the sum and product of
20
terms in G.P. are
16
and
1024
respectively, then the sum of its reciprocals is
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Solution
S
=
a
+
a
r
+
a
r
2
+
⋯
+
a
r
n
−
1
⇒
S
=
a
(
r
n
−
1
)
r
−
1
⇒
a
(
r
20
−
1
)
r
−
1
=
16
⋯
(
1
)
P
=
a
.
a
r
.
a
r
2
.
.
.
a
n
−
1
⇒
P
=
a
n
.
r
1
+
2
+
3
+
⋯
+
(
n
−
1
)
=
a
n
.
r
(
n
−
1
)
n
2
⇒
a
20
r
190
=
1024
Now, assuming
R
=
1
a
+
1
a
r
+
⋯
+
1
a
r
n
−
1
⇒
R
=
1
a
(
(
1
r
)
20
−
1
)
1
r
−
1
⇒
R
=
a
(
1
−
r
20
)
a
2
r
19
(
1
−
r
)
⇒
R
=
16
(
1024
)
1
/
10
∴
R
=
16
2
=
8
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