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Byju's Answer
Standard X
Mathematics
Properties of GP
Sum 1 + 3x ...
Question
Sum
1
+
3
x
+
5
x
2
+
7
x
3
+
9
x
4
+
.
.
.
.
to infinity.
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Solution
Let
S
=
1
+
3
x
+
5
x
2
+
7
x
3
.
.
.
.
.
.
∞
Multiplying both sides by
a
, we get
S
x
=
0
+
x
+
3
x
2
+
5
x
3
.
.
.
.
.
.
.
∞
Subtract both eqns, we get
S
(
1
−
x
)
=
1
+
2
(
x
+
x
2
+
x
3
.
.
.
.
.
.
.
∞
)
Clearly, the series in the bracket is a G.P. with common ratio
=
x
∴
S
(
1
−
x
)
=
1
+
2
x
1
−
x
=
1
+
x
1
−
x
⇒
S
=
1
+
x
(
1
−
x
)
2
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0
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Sum
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.
.
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