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Byju's Answer
Standard XII
Mathematics
nCr Definitions and Properties
Find the valu...
Question
Find the value of :
1
×
1
!
+
2
×
2
!
+
3
×
3
!
+
.
.
.
.
.
.
.
+
n
×
n
!
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Solution
1
×
1
!
=
(
2
−
1
)
×
1
!
=
2
×
1
!
−
1
×
1
!
=
2
!
−
1
!
2
×
2
!
=
(
3
−
1
)
×
2
!
=
3
×
2
!
−
2
!
=
3
!
−
2
!
3
×
3
!
=
(
4
−
1
)
×
3
!
=
4
×
3
!
−
3
!
=
4
!
−
3
!
n
×
n
!
=
(
n
+
1
−
1
)
×
n
!
=
(
n
+
1
)
(
n
!
)
−
n
!
=
(
n
+
1
)
!
−
n
!
Summing up all these terms, we get
=
2
!
−
1
!
+
3
!
−
2
!
+
4
!
−
3
!
+
.
.
.
+
(
n
+
1
)
!
−
n
!
=
(
n
+
1
)
!
−
1
!
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