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Byju's Answer
Standard XII
Mathematics
Sum of n Terms
The sum of th...
Question
The sum of the series
(
1
2
+
1
)
.1
!
+
(
2
2
+
1
)
.2
!
+
(
3
2
+
1
)
.3
!
+
.
.
.
.
+
(
n
2
+
1
)
.
n
!
i
s
:
A
(n + 1). (n+2)!
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B
n.(n+1)!
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C
(n + 1). (n+1)!
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D
none of these
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Solution
The correct option is
B
n.(n+1)!
T
n
= [ n (n + 1) - (n - 1) ] n! = n.(n+1)! - (n - 1).n!
Now put n = 1, 2, 3, ...... , n and add
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5
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