Mister Exam

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Sum of series:
f(x)
(-p+5h-2,5g)*1,5n
f(xi)
e^(nx)
Derivative of:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)
fx
Similar expressions
f(xi)
f*x^n/(3(n+4))

Sum of series/ f(x)

Sum of series f(x)

The solution

You have entered [src]

  oo     
 __      
 \ `     
  )   f*x
 /_,     
x = 1

\sum_{x=1}^{\infty} f x

Sum(f*x, (x, 1, oo))

The radius of convergence of the power series

Given number:

f x

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} = f x

and

x_{0} = 0

,

d = 0

,

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{x}{x + 1}\right)

Let's take the limit
we find

True

False

The answer [src]

oo*f

\infty f

oo*f

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
```