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Tardigrade
Question
Mathematics
Let tn denotes the n th term of the infinite series (1/1 !)+(10/2 !)+(21/3 !)+(34/4 !)+(49/5 !)+ ldots. Then, displaystyle lim n arrow ∞ tn is
Q. Let
t
n
denotes the
n
t
h
term of the infinite series
1
!
1
+
2
!
10
+
3
!
21
+
4
!
34
+
5
!
49
+
…
. Then,
n
→
∞
lim
t
n
is
1640
212
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WBJEE 2014
Limits and Derivatives
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A
e
B
0
C
e
2
D
1
Solution:
Let
S
=
1
+
10
+
21
+
34
+
49
+
…
+
t
n
′
and
S
=
1
+
10
+
21
+
34
+
…
+
t
n
′
0
=
1
+
9
+
11
+
13
+
15
+
…
−
t
n
′
⇒
t
n
′
=
1
+
[
9
+
11
+
13
+
15
+
…
(
n
−
1
)
term
]
=
1
+
[
2
n
−
1
{
2
×
9
+
(
n
−
2
)
2
}
]
=
1
+
(
n
−
1
)
[
9
+
n
−
2
]
=
1
+
(
n
−
1
)
(
n
+
7
)
∴
t
n
=
n
!
t
n
′
=
n
!
1
+
(
n
−
1
)
(
n
+
7
)
=
n
!
1
+
(
n
−
1
)
(
n
+
7
)
=
n
!
1
+
n
2
+
6
n
−
7
=
n
!
n
2
+
6
n
−
6
=
(
n
−
1
)!
n
˙
+
(
n
−
1
)!
6
−
n
!
1
=
(
n
−
1
)!
n
−
1
+
1
+
(
n
−
1
)!
6
−
n
!
1
=
(
n
−
2
)!
1
+
(
n
−
1
)!
7
−
n
!
1
∴
n
→
∞
lim
t
n
=
n
→
∞
lim
[
(
n
−
2
)!
1
+
(
n
−
1
)!
7
−
n
!
1
]
′
=
0