Mister Exam

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Sum of series:
15
cos(x+y)
1/(x*ln(x)^2)
1/((3n-2)*(3n+1))
The double integral of:
cos(x+y)
cos(x+y)
Integral of d{x}:
cos(x+y)
Identical expressions
cos(x+y)
co sinus of e of (x plus y)
cosx+y
Similar expressions
1/(cos(x)+y)
cos(x-y)

Sum of series/ cos(x+y)

Sum of series cos(x+y)

The solution

You have entered [src]

  oo            
 __             
 \ `            
  )   cos(x + y)
 /_,            
n = 1

\sum_{n=1}^{\infty} \cos{\left(x + y \right)}

Sum(cos(x + y), (n, 1, oo))

The radius of convergence of the power series

Given number:

\cos{\left(x + y \right)}

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} = \cos{\left(x + y \right)}

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*cos(x + y)

\infty \cos{\left(x + y \right)}

oo*cos(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
```