Mister Exam
Other calculators
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How to use it?
- Sum of series:
- (2^n+3^n)/6^n
- 1/n!
- x^n/2^n
- 1/(3n-2)*(3n+1)
-
Identical expressions
- one /n!
- 1 divide by n!
- one divide by n!
-
Similar expressions
- cos(n*0.1)/n!
- ((-1)^(n+1)/(n!(n+0.5)))(2^(-n-0.5)-1)
- 1/(n!)^100
- ((-1)^(n+1))/(n!)
- (2n+1)/n!
Sum of series 1/n!
The solution
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oo ___ \ ` \ 1 ) -- / n! /__, n = 1
$$\sum_{n=1}^{\infty} \frac{1}{n!}$$
Sum(1/factorial(n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{n!}$$
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
$$a_{n} = \frac{1}{n!}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{\left(n + 1\right)!}{n!}}\right|$$
Let's take the limit
we find
$$\frac{1}{n!}$$
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
$$a_{n} = \frac{1}{n!}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{\left(n + 1\right)!}{n!}}\right|$$
Let's take the limit
we find
False
False
The rate of convergence of the power series
The graph