Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
(-1)^n*(2*2)^(2*n)/factorial(2*n)
k^2
log(n+1)/(n+1)
sin((n+1)/(2*n-1))^2
Identical expressions
fourteen ^49n2-56n- thirty-three
14 to the power of 49n2 minus 56n minus 33
fourteen to the power of 49n2 minus 56n minus thirty minus three
1449n2-56n-33
14⁴9n2-56n-33
Similar expressions
14^49n2+56n-33
14^49n2-56n+33

Sum of series 14^49n2-56n-33

The solution

You have entered [src]

  oo                                                                            
 __                                                                             
 \ `                                                                            
  )   (144635115998316938222768918983913092176221616624719888384*n2 - 56*n - 33)
 /_,                                                                            
n = 1

\sum_{n=1}^{\infty} \left(\left(- 56 n + 144635115998316938222768918983913092176221616624719888384 n_{2}\right) - 33\right)

Sum(144635115998316938222768918983913092176221616624719888384*n2 - 56*n - 33, (n, 1, oo))

The radius of convergence of the power series

Given number:

\left(- 56 n + 144635115998316938222768918983913092176221616624719888384 n_{2}\right) - 33

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} = - 56 n + 144635115998316938222768918983913092176221616624719888384 n_{2} - 33

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} \left|{\frac{56 n - 144635115998316938222768918983913092176221616624719888384 n_{2} + 33}{56 n - 144635115998316938222768918983913092176221616624719888384 n_{2} + 89}}\right|

Let's take the limit
we find

True

False

The answer [src]

-oo + oo*(-33 + 144635115998316938222768918983913092176221616624719888384*n2)

\infty \left(144635115998316938222768918983913092176221616624719888384 n_{2} - 33\right) - \infty

-oo + oo*(-33 + 144635115998316938222768918983913092176221616624719888384*n2)

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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series 14^49n2-56n-33

The solution

Examples of finding the sum of a series