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Byju's Answer
Standard XII
Mathematics
Sum of Coefficients of All Terms
Find the sum ...
Question
Find the sum of n terms of the series
1
+
2
x
+
3
x
2
+
4
x
3
+
5
x
4
+
.
.
.
.
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Solution
The series is the expansion of
(
1
−
x
)
−
2
∴
S
n
=
1
+
2
x
+
3
x
2
+
.
.
.
.
+
n
x
n
−
1
−
2
x
S
n
=
−
2
x
−
4
x
2
−
6
x
3
−
.
.
.
.
.
.
−
2
(
n
−
1
)
x
n
−
1
−
2
n
x
n
x
2
S
n
=
x
2
+
2
x
3
+
.
.
.
.
+
(
n
−
2
)
x
n
−
1
+
(
x
−
1
)
x
n
+
n
x
n
+
1
;
S
n
(
1
−
x
)
2
=
1
−
(
n
+
1
)
x
n
+
n
x
n
+
1
∴
S
n
=
1
−
x
n
(
1
−
x
)
2
−
n
x
n
1
−
x
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