Mister Exam

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How to use it?
Sum of series:
n^2*x^n/4^n
(3x)^2n/ln(2n-1)
(16-16cos(3(pi)n/4)/(pi^2n^2))cos(n(pi))
sqrt(x)/(100^2+x)
Identical expressions
sqrt(x)/(one hundred ^ two +x)
square root of (x) divide by (100 squared plus x)
square root of (x) divide by (one hundred to the power of two plus x)
√(x)/(100^2+x)
sqrt(x)/(1002+x)
sqrtx/1002+x
sqrt(x)/(100²+x)
sqrt(x)/(100 to the power of 2+x)
sqrtx/100^2+x
sqrt(x) divide by (100^2+x)
Similar expressions
sqrt(x)/(100^2-x)

Sum of series/ sqrt(x)/(100^2+x)

Sum of series sqrt(x)/(100^2+x)

The solution

You have entered [src]

  oo           
____           
\   `          
 \        ___  
  \     \/ x   
  /   ---------
 /    10000 + x
/___,          
x = 1

$$\sum_{x=1}^{\infty} \frac{\sqrt{x}}{x + 10000}$$

Sum(sqrt(x)/(10000 + x), (x, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{\sqrt{x}}{x + 10000}$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = \frac{\sqrt{x}}{x + 10000}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\frac{\sqrt{x} \left(x + 10001\right)}{\sqrt{x + 1} \left(x + 10000\right)}\right)$$
Let's take the limit
we find

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series sqrt(x)/(100^2+x)

The solution

Examples of finding the sum of a series