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Byju's Answer
Standard VIII
Mathematics
Division of a Polynomial by a Monomial
Find the gene...
Question
Find the generating functions of the series
1
4
+
2
4
x
+
3
4
x
2
+
4
4
x
3
+
5
4
x
4
+
.
.
.
.
Open in App
Solution
S
=
1
+
16
x
+
81
x
2
+
256
x
3
+
625
x
4
+
1296
x
5
…
−
5
x
S
=
−
5
x
−
80
x
2
−
405
x
3
−
1280
x
4
−
3125
x
5
−
…
10
x
2
S
=
10
x
2
+
160
x
3
+
810
x
4
+
2560
x
5
+
…
−
10
x
3
S
=
−
10
x
3
−
160
x
4
−
810
x
5
−
…
5
x
4
S
=
5
x
4
+
80
x
5
+
…
−
x
5
S
=
−
x
5
−
…
Adding the above series, we get
(
1
−
3
x
+
10
x
2
−
10
x
3
+
5
x
4
−
x
5
)
S
=
1
+
11
x
+
11
x
2
+
x
3
⟹
(
1
−
x
)
5
S
=
1
+
11
x
+
11
x
2
+
x
3
⟹
S
=
1
+
11
x
+
11
x
2
+
x
3
(
1
−
x
)
5
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