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Byju's Answer
Standard XII
Mathematics
Sum of Coefficients of All Terms
Find the r+...
Question
Find the
(
r
+
1
)
t
h
term in each of the following expansion :
1
√
1
+
2
x
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Solution
The general term i.e.
(
r
+
1
)
t
h
term in the expansion of
(
1
+
x
)
n
is given by
T
r
+
1
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
.
(
n
−
r
+
1
)
r
!
x
r
Now,
1
√
1
+
2
x
=
(
1
+
2
x
)
−
1
2
T
r
+
1
=
−
1
2
(
−
1
2
−
1
)
(
−
1
2
−
2
)
(
−
1
2
−
3
)
.
.
.
.
.
.
.
.
.
.
(
−
1
2
−
r
+
1
)
r
!
(
2
x
)
r
=
(
−
1
)
(
−
3
)
(
−
5
)
(
−
7
)
.
.
.
.
.
.
.
.
(
1
−
2
r
)
2
r
.
r
!
2
r
.
x
r
=
(
−
1
)
r
1.3.5.7.......
(
2
r
−
1
)
r
!
x
r
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