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Byju's Answer
Standard XII
Mathematics
Summation by Sigma Method
Sum of infini...
Question
Sum of infinity the following series:
1
+
4
x
2
+
7
x
4
+
10
x
6
+
.
.
.
,
|
x
|
<
1
.
Open in App
Solution
S
=
1
+
4
x
2
+
7
x
4
+
10
x
6
+
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(
1
)
S
x
2
=
x
2
+
4
x
4
+
7
x
6
+
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(
2
)
e
q
n
(
1
)
–
e
q
n
(
2
)
, we get
(
1
–
x
2
)
S
=
1
+
3
x
2
+
3
x
4
+
3
x
6
+
…
.
.
.
.
.
.
.
.
.
.
.
.
(
3
)
This is a
G
.
P
. of common ratio
=
x
2
So, using sum of
G
.
P
.
=
a
(
1
−
r
)
Here,
a
=
f
i
r
s
t
t
e
r
m
and
r
=
c
o
m
m
o
n
r
a
t
i
o
So,
(
1
–
x
2
)
S
=
1
+
3
x
2
(
1
–
x
2
)
(
1
–
x
2
)
S
=
1
−
x
2
+
3
x
2
(
1
–
x
2
)
S
=
1
+
2
x
2
(
1
–
x
2
)
2
Hence, this is the answer.
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