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Byju's Answer
Standard XII
Mathematics
A.G.P
If the sum of...
Question
If the sum of the series
1
+
2
r
+
3
r
2
+
4
r
3
+
⋯
∞
is
9
4
,
then the value of
r
is
A
1
2
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B
1
3
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C
1
4
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D
5
3
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Solution
The correct option is
B
1
3
S
=
1
+
2
r
+
3
r
2
+
4
r
3
+
…
r
S
=
r
+
2
r
2
+
3
r
3
+
4
r
4
+
…
⇒
(
1
−
r
)
S
=
1
+
r
+
r
2
+
r
3
+
…
⇒
(
1
−
r
)
S
=
1
1
−
r
provided
|
r
|
<
1
⇒
S
=
1
(
1
−
r
)
2
Given,
S
=
9
4
⇒
1
(
1
−
r
)
2
=
9
4
⇒
1
−
r
=
±
2
3
⇒
r
=
1
3
,
5
3
∴
r
=
1
3
(
∵
|
r
|
<
1
)
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