Mister Exam

Other calculators


(-8)^(n+1)/(n+1)!

Sum of series (-8)^(n+1)/(n+1)!



=

The solution

You have entered [src]
  oo           
____           
\   `          
 \        n + 1
  \   (-8)     
  /   ---------
 /     (n + 1)!
/___,          
n = 1          
$$\sum_{n=1}^{\infty} \frac{\left(-8\right)^{n + 1}}{\left(n + 1\right)!}$$
Sum((-8)^(n + 1)/factorial(n + 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\left(-8\right)^{n + 1}}{\left(n + 1\right)!}$$
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
$$a_{n} = \frac{\left(-8\right)^{n + 1}}{\left(n + 1\right)!}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(8^{- n - 2} \cdot 8^{n + 1} \left|{\frac{\left(n + 2\right)!}{\left(n + 1\right)!}}\right|\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src]
     -8
7 + e  
$$e^{-8} + 7$$
7 + exp(-8)
Numerical answer [src]
7.00033546262790251183882138913
7.00033546262790251183882138913
The graph
Sum of series (-8)^(n+1)/(n+1)!

    Examples of finding the sum of a series