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Byju's Answer
Standard XII
Mathematics
Method of Difference
If 1/1!9! +...
Question
If
1
1
!
9
!
+
1
3
!
7
!
+
1
5
!
5
!
+
1
7
!
3
!
+
1
9
!
1
!
=
2
n
10
!
Then n
=
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Solution
Given,
1
1
!
9
!
+
1
3
!
7
!
+
1
5
!
5
!
+
1
7
!
3
!
+
1
9
!
1
!
=
2
n
10
!
10
!
1
!
⋅
9
!
+
10
!
3
!
⋅
7
!
+
10
!
5
!
⋅
5
!
+
10
!
7
!
⋅
3
!
+
10
!
9
!
⋅
1
!
=
2
n
20
1
!
+
1440
3
!
+
10
!
5
!
⋅
5
!
=
2
n
20
1
!
+
1440
3
!
+
30240
5
!
=
2
n
20
1
+
1440
6
+
30240
120
=
2
n
2400
+
28800
+
30240
120
=
2
n
512
=
2
n
2
9
=
2
n
∴
n
=
9
Suggest Corrections
0
Similar questions
Q.
If
1
1
!
9
!
+
1
3
!
7
!
+
1
5
!
5
!
+
1
9
!
1
!
=
2
n
10
!
Then
n
=
Q.
(
1
+
3
1
)
(
1
+
5
4
)
(
1
+
7
9
)
⋯
(
1
+
(
2
n
+
1
)
n
2
)
=
(
n
+
1
)
2
Q.
Show that
1
+
1
2
+
1
3
+
⋯
+
1
n
+
1
=
1
1
−
1
3
−
4
5
−
9
7
−
⋯
n
2
2
n
+
1
.
Q.
Convert the following products into factorials:
(i) 5 · 6 · 7 · 8 · 9 · 10
(ii) 3 · 6 · 9 · 12 · 15 · 18
(iii) (n + 1) (n + 2) (n + 3) ... (2n)
(iv) 1 · 3 · 5 · 7 · 9 ... (2n − 1)
Q.
If
S
n
=
1
1
⋅
3
⋅
5
+
1
3
⋅
5
⋅
7
+
1
5
⋅
7
⋅
9
⋯
, then
24
S
∞
=
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