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1/1^4+1/4^7+1/7^10+

  • How to use it?

  • Sum of series:
  • (-1)^n (-1)^n
  • 1/(n(n+3)) 1/(n(n+3))
  • (3^n-4^n)/12^n (3^n-4^n)/12^n
  • 1/((n+14)(n+15)) 1/((n+14)(n+15))

  • Identical expressions

  • one / one ^ four + one / four ^ seven + one / seven ^ ten +
  • 1 divide by 1 to the power of 4 plus 1 divide by 4 to the power of 7 plus 1 divide by 7 to the power of 10 plus
  • one divide by one to the power of four plus one divide by four to the power of seven plus one divide by seven to the power of ten plus
  • 1/14+1/47+1/710+
  • 1/1⁴+1/4⁷+1/7^10+
  • 1 divide by 1^4+1 divide by 4^7+1 divide by 7^10+

  • Similar expressions

  • 1/1^4+1/4^7-1/7^10+
  • 1/1^4+1/4^7+1/7^10-
  • 1/1^4-1/4^7+1/7^10+
Sum of series/ 1/1^4+1/4^7+1/7^10+

Sum of series 1/1^4+1/4^7+1/7^10+


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The solution

You have entered [src] 
  oo                 
____                 
\   `                
 \    / 4   1     1 \
  \   |1  + -- + ---|
  /   |      7    10|
 /    \     4    7  /
/___,                
n = 1
$$\sum_{n=1}^{\infty} \left(\left(\frac{1}{7}\right)^{10} + \left(\left(\frac{1}{4}\right)^{7} + 1^{4}\right)\right)$$ 
Sum(1^4 + (1/4)^7 + (1/7)^10, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{1}{7}\right)^{10} + \left(\left(\frac{1}{4}\right)^{7} + 1^{4}\right)$$
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
$$a_{n} = \frac{4628356971249}{4628074479616}$$
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 rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
Numerical answer
The series diverges
The graph
Sum of series 1/1^4+1/4^7+1/7^10+

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