Tardigrade
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Tardigrade
Question
Mathematics
displaystyle lim n arrow ∞ (nk sin 2(n !)/n+2) 0 < k < 1, is equal to
Q.
n
→
∞
lim
n
+
2
n
k
sin
2
(
n
!)
0
<
k
<
1
, is equal to
2001
216
Limits and Derivatives
Report Error
A
∞
B
1
C
0
D
None of these
Solution:
n
→
∞
lim
n
+
2
n
k
sin
2
(
n
!)
=
n
→
∞
lim
n
(
1
+
n
2
)
n
k
sin
2
(
n
!)
=
n
→
∞
lim
n
1
−
k
(
1
+
n
2
)
sin
2
(
n
!)
=
∞
a finite quantity
[
∵
sin
2
(
n
!)
always lies between
0
and
1
.
Also, since
1
−
k
>
0
,
∴
n
1
−
k
→
∞
as
n
→
∞
]
=
0.