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Byju's Answer
Standard XII
Mathematics
Removable Discontinuities
lim #8203;n...
Question
lim
n->inf.
(-1)
n
sin(n(n
2
+5n+1)
1/2
)
Open in App
Solution
Dear student
lim
n
→
∞
(
-
1
)
n
sin
(
n
n
2
+
5
n
+
1
)
(
-
1
)
n
o
s
c
i
l
l
a
t
e
s
b
e
t
w
e
e
n
-
1
a
n
d
1
a
s
n
t
e
n
d
s
t
o
i
n
f
i
n
i
t
y
a
n
d
i
s
f
i
n
i
t
e
l
y
b
o
u
n
d
e
d
w
h
e
r
e
a
s
i
n
t
h
e
s
e
c
o
n
d
t
e
r
m
,
sin
o
s
c
i
l
l
a
t
e
s
b
e
t
w
e
e
n
-
1
a
n
d
1
s
o
lim
n
→
∞
(
-
1
)
n
sin
(
n
n
2
+
5
n
+
1
)
o
s
c
i
l
l
a
t
e
s
b
e
t
w
e
e
n
-
1
a
n
d
1
a
n
d
i
s
u
n
d
e
f
i
n
e
d
Regards
Suggest Corrections
0
Similar questions
Q.
If the equation
x
n
−
1
=
0
,
n
>
1
,
n
∈
N
,
has roots
1
,
a
1
,
a
2
,
…
,
a
n
−
1
,
then
Q.
If
∑
5
n
=
1
1
n
(
n
+
1
)
(
n
+
2
)
(
n
+
3
)
=
k
3
, then k is equal to?
Q.
The equation
x
n
=
1
,
n
>
1
,
n
∈
N
has roots
1
,
a
1
,
a
2
,
.
.
.
,
a
n
−
1
. Then which of the following are correct?
Q.
Evaluate
lim
n
→
∞
(
−
1
)
n
−
1
s
i
n
(
π
√
n
2
+
0.5
n
+
1
)
, where
n
∈
N
.
Q.
If n is a multiple of
3
, show that
1
−
n
−
3
2
+
(
n
−
4
)
(
n
−
5
)
⌊
3
−
(
n
−
5
)
(
n
−
6
)
(
n
−
7
)
⌊
4
+
.
.
.
.
.
+
(
−
1
)
r
−
1
(
n
−
r
−
1
)
(
n
−
r
−
2
)
.
.
.
.
(
n
−
2
r
+
1
)
⌊
r
+
.
.
.
.
.
.
,
is equal to
3
n
or
−
1
n
, according as n is odd or even.
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