Mister Exam
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Limit of the function
:
Limit of ((1+x)/(1+2*x))^x
Limit of (9^x-8^x)/asin(3*x)
Limit of ((5+6*x)/(-10+x))^(5*x)
Limit of (-2+x)^(-2)
Sum of series
:
(-1)^n/sqrt(n)
Identical expressions
(- one)^n/sqrt(n)
( minus 1) to the power of n divide by square root of (n)
( minus one) to the power of n divide by square root of (n)
(-1)^n/√(n)
(-1)n/sqrt(n)
-1n/sqrtn
-1^n/sqrtn
(-1)^n divide by sqrt(n)
Similar expressions
(1)^n/sqrt(n)
Limit of the function
/
(-1)^n/sqrt(n)
Limit of the function (-1)^n/sqrt(n)
at
→
Calculate the limit!
v
For end points:
---------
From the left (x0-)
From the right (x0+)
The graph:
from
to
Piecewise:
{
enter the piecewise function here
The solution
You have entered
[src]
/ n\ |(-1) | lim |-----| n->oo| ___| \\/ n /
lim
n
→
∞
(
(
−
1
)
n
n
)
\lim_{n \to \infty}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right)
n
→
∞
lim
(
n
(
−
1
)
n
)
Limit((-1)^n/(sqrt(n)), n, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
0
2
4
6
8
-8
-6
-4
-2
-10
10
0.31
0.33
Plot the graph
Rapid solution
[src]
None
None
Expand and simplify
Other limits n→0, -oo, +oo, 1
lim
n
→
∞
(
(
−
1
)
n
n
)
\lim_{n \to \infty}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right)
n
→
∞
lim
(
n
(
−
1
)
n
)
lim
n
→
0
−
(
(
−
1
)
n
n
)
=
−
∞
i
\lim_{n \to 0^-}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right) = - \infty i
n
→
0
−
lim
(
n
(
−
1
)
n
)
=
−
∞
i
More at n→0 from the left
lim
n
→
0
+
(
(
−
1
)
n
n
)
=
∞
\lim_{n \to 0^+}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right) = \infty
n
→
0
+
lim
(
n
(
−
1
)
n
)
=
∞
More at n→0 from the right
lim
n
→
1
−
(
(
−
1
)
n
n
)
=
−
1
\lim_{n \to 1^-}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right) = -1
n
→
1
−
lim
(
n
(
−
1
)
n
)
=
−
1
More at n→1 from the left
lim
n
→
1
+
(
(
−
1
)
n
n
)
=
−
1
\lim_{n \to 1^+}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right) = -1
n
→
1
+
lim
(
n
(
−
1
)
n
)
=
−
1
More at n→1 from the right
lim
n
→
−
∞
(
(
−
1
)
n
n
)
\lim_{n \to -\infty}\left(\frac{\left(-1\right)^{n}}{\sqrt{n}}\right)
n
→
−
∞
lim
(
n
(
−
1
)
n
)
More at n→-oo
The graph