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(n^(4)+n^(3)1)^(1/4)*sin(1/(n^4)^(1/3))

  • How to use it?

  • Sum of series:
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  • 1/(2*n-1)*(2*n+1) 1/(2*n-1)*(2*n+1)
  • cos(kx)
  • ((-1)^(n-1))*(5^n+2)*x^n

  • Identical expressions

  • (n^(four)+n^(three) one)^(one / four)*sin(one /(n^ four)^(one / three))
  • (n to the power of (4) plus n to the power of (3)1) to the power of (1 divide by 4) multiply by sinus of (1 divide by (n to the power of 4) to the power of (1 divide by 3))
  • (n to the power of (four) plus n to the power of (three) one) to the power of (one divide by four) multiply by sinus of (one divide by (n to the power of four) to the power of (one divide by three))
  • (n(4)+n(3)1)(1/4)*sin(1/(n4)(1/3))
  • n4+n311/4*sin1/n41/3
  • (n^(4)+n^(3)1)^(1/4)*sin(1/(n⁴)^(1/3))
  • (n^(4)+n^(3)1)^(1/4)sin(1/(n^4)^(1/3))
  • (n(4)+n(3)1)(1/4)sin(1/(n4)(1/3))
  • n4+n311/4sin1/n41/3
  • n^4+n^31^1/4sin1/n^4^1/3
  • (n^(4)+n^(3)1)^(1 divide by 4)*sin(1 divide by (n^4)^(1 divide by 3))

  • Similar expressions

  • (n^(4)-n^(3)1)^(1/4)*sin(1/(n^4)^(1/3))
Sum of series/ (n^(4)+n^(3)1)^(1/4)*sin(1/(n^4)^(1/3))

Sum of series (n^(4)+n^(3)1)^(1/4)*sin(1/(n^4)^(1/3))


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The solution

You have entered [src] 
  oo                            
_____                           
\    `                          
 \        _________             
  \    4 /  4    3     /   1   \
   \   \/  n  + n  *sin|-------|
   /                   |   ____|
  /                    |3 /  4 |
 /                     \\/  n  /
/____,                          
n = 1
$$\sum_{n=1}^{\infty} \sqrt[4]{n^{4} + n^{3}} \sin{\left(\frac{1}{\sqrt[3]{n^{4}}} \right)}$$ 
Sum((n^4 + n^3)^(1/4)*sin(1/((n^4)^(1/3))), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\sqrt[4]{n^{4} + n^{3}} \sin{\left(\frac{1}{\sqrt[3]{n^{4}}} \right)}$$
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
$$a_{n} = \sqrt[4]{n^{4} + n^{3}} \sin{\left(\frac{1}{\sqrt[3]{n^{4}}} \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\sqrt[4]{n^{4} + n^{3}} \left|{\frac{\sin{\left(\frac{1}{n^{\frac{4}{3}}} \right)}}{\sin{\left(\frac{1}{\left(n + 1\right)^{\frac{4}{3}}} \right)}}}\right|}{\sqrt[4]{\left(n + 1\right)^{4} + \left(n + 1\right)^{3}}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  oo                        
____                        
\   `                       
 \       _________          
  \   4 /  3    4     / 1  \
   )  \/  n  + n  *sin|----|
  /                   | 4/3|
 /                    \n   /
/___,                       
n = 1
$$\sum_{n=1}^{\infty} \sqrt[4]{n^{4} + n^{3}} \sin{\left(\frac{1}{n^{\frac{4}{3}}} \right)}$$ 
Sum((n^3 + n^4)^(1/4)*sin(n^(-4/3)), (n, 1, oo))
The graph
Sum of series (n^(4)+n^(3)1)^(1/4)*sin(1/(n^4)^(1/3))

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