Mister Exam

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Sum of series:
sin(nx)*(5-(3*n))
e^(4n)
(-1)^n*pi^(2n)/((2n)!)
cosnx/n^p
Identical expressions
(- one)^n*pi^(2n)/((2n)!)
( minus 1) to the power of n multiply by Pi to the power of (2n) divide by ((2n)!)
( minus one) to the power of n multiply by Pi to the power of (2n) divide by ((2n)!)
(-1)n*pi(2n)/((2n)!)
-1n*pi2n/2n!
(-1)^npi^(2n)/((2n)!)
(-1)npi(2n)/((2n)!)
-1npi2n/2n!
-1^npi^2n/2n!
(-1)^n*pi^(2n) divide by ((2n)!)
Similar expressions
(1)^n*pi^(2n)/((2n)!)

Sum of series (-1)^n*pi^(2n)/((2n)!)

You have entered [src]

  oo             
____             
\   `            
 \        n   2*n
  \   (-1) *pi   
  /   -----------
 /       (2*n)!  
/___,            
n = 1

\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n} \pi^{2 n}}{\left(2 n\right)!}

Sum(((-1)^n*pi^(2*n))/factorial(2*n), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{\left(-1\right)^{n} \pi^{2 n}}{\left(2 n\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} = \frac{\left(-1\right)^{n}}{\left(2 n\right)!}

and

x_{0} = - \pi

d = 2

c = 0

then

R^{2} = \tilde{\infty} \left(- \pi + \lim_{n \to \infty} \left|{\frac{\left(2 n + 2\right)!}{\left(2 n\right)!}}\right|\right)

R^{2} = \infty

R = \infty

The rate of convergence of the power series

The answer [src]

-2

-2

-2

Numerical answer [src]

-2.00000000000000000000000000000

-2.00000000000000000000000000000

The graph