Mister Exam

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How to use it?
Sum of series:
n^n/2^(n+1)
e^(-n)
1/((3n+1)*(3n+4))
1/((2*n-1)(2*n+1))
Integral of d{x}:
x/x^2
Canonical form:
x/x^2
Identical expressions
x/x^ two
x divide by x squared
x divide by x to the power of two
x/x2
x/x²
x/x to the power of 2
x divide by x^2

Sum of series/ x/x^2

Sum of series x/x^2

The solution

You have entered [src]

  oo    
____    
\   `   
 \    x 
  \   --
  /    2
 /    x 
/___,   
n = 1

\sum_{n=1}^{\infty} \frac{x}{x^{2}}

Sum(x/x^2, (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{x}{x^{2}}

It is a series of species

a_{n} \left(c x - x_{0}\right)^{d n}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}

In this case

a_{n} = \frac{1}{x}

and

x_{0} = 0

,

d = 0

,

c = 1

then

1 = \lim_{n \to \infty} 1

Let's take the limit
we find

True

False

The answer [src]

oo
--
x

\frac{\infty}{x}

oo/x

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
```