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Byju's Answer
Standard XII
Mathematics
Rational Function
The sum ∑10...
Question
The sum
∑
10
k
=
1
k.k! equals
A
(10)!
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B
(11)!
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C
(10)! + 1
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D
(11)! - 1
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Solution
The correct option is
D
(11)! - 1
∑
10
k
=
1
k
.
k
!
=
1.1
!
+
2.2
!
+
3.3
!
+
.
.
.
.
.10
.10
!
First term can be written as difference of
1
.
=
(
2
−
1
)
!
+
(
3
−
1
)
2
!
+
(
4
−
1
)
3
!
+
.
.
.
.
.
.
(
11
−
1
)
10
!
=
2
!
−
1
!
+
3
!
−
2
!
+
4
!
−
3
!
+
.
.
.
.
.
.
.11
!
−
10
!
only two terms are left
=
11
!
−
1
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0
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