Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
x*y
exp(n)
(1)/(2^n+n)
-8
x*y
Integral of d{x}:
x*y
Limit of the function:
x*y
Identical expressions
x*y
x multiply by y
xy
Similar expressions
(xy)n
(x^z-m^x)(y^z-m^y)
x^y/y!

Sum of series/ x*y

Sum of series x*y

The solution

You have entered [src]

  oo     
 __      
 \ `     
  )   x*y
 /_,     
n = 0

\sum_{n=0}^{\infty} x y

Sum(x*y, (n, 0, oo))

The radius of convergence of the power series

Given number:

x y

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} = x y

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*y

\infty x y

oo*x*y

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
```