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Byju's Answer
Standard XII
Mathematics
Finding Integral Part of Numbers of the Form a^b Where a Is Irrational
The value of ...
Question
The value of
1
1
!
(
n
−
1
)
!
+
1
3
!
(
n
−
3
)
!
+
…
+
1
(
n
−
1
)
!
(
1
)
!
, where
n
is even positive integer, is
A
2
n
(
n
−
1
)
!
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B
2
n
−
1
n
!
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C
2
n
+
1
n
!
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D
2
n
(
n
+
1
)
!
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Solution
The correct option is
B
2
n
−
1
n
!
Let
S
=
1
1
!
(
n
−
1
)
!
+
1
3
!
(
n
−
3
)
!
+
…
+
1
(
n
−
1
)
!
(
1
)
!
⇒
S
=
1
n
!
[
n
!
1
!
(
n
−
1
)
!
+
n
!
3
!
(
n
−
3
)
!
+
…
+
n
!
(
n
−
1
)
!
(
1
)
!
]
⇒
S
=
1
n
!
[
n
C
1
+
n
C
3
+
…
+
n
C
n
−
1
]
∴
S
=
2
n
−
1
n
!
Suggest Corrections
12
Similar questions
Q.
Prove that
1
−
2
n
+
2
n
(
2
n
−
1
)
2
!
−
2
n
(
2
n
−
1
)
(
2
n
−
1
)
3
!
+
.
.
.
+
(
−
1
)
n
−
1
2
n
(
n
−
1
)
.
.
.
(
n
+
2
)
(
n
−
1
)
=
(
−
1
)
n
+
1
(
2
n
)
2
(
n
!
)
2
,
where n is a + ive integer.
Q.
Prove that if
n
be an even integer,
1
|
1
–
|
n
−
1
–
––––
–
+
1
|
3
–
|
n
−
3
–
––––
–
+
1
|
5
–
|
n
−
5
–
––––
–
+
.
.
.
.
+
1
|
n
−
1
–
––––
–
|
1
–
=
2
n
−
1
|
n
–
–
.
Q.
The coefficient of
1
x
in the expansion of
1
+
x
n
1
+
1
x
n
is
(a)
n
!
n
-
1
!
n
+
1
!
(b)
2
n
!
n
-
1
!
n
+
1
!
(c)
2
n
!
2
n
-
1
!
2
n
+
1
!
(d) none of these
Q.
The coefficient of
1
x
in the expansion of
(
1
+
x
)
n
(
1
+
1
x
)
n
is
Q.
If n is a positive integer, then
2
n
>
1
+
n
√
(
2
n
−
1
)
.
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Finding Integral Part of Numbers of the Form a^b Where a Is Irrational
Standard XII Mathematics
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