Mister Exam

Lang:

How to use it?
Sum of series:
(13^(2n-1))/((2^n)*(n-1)!)
(5^n-4^n)/20^n
x^n/(1+x^n)
x^(n-1)/(n!)^(1/2)
Identical expressions
sin^ two (x)/(x^(one / three))
sinus of squared (x) divide by (x to the power of (1 divide by 3))
sinus of to the power of two (x) divide by (x to the power of (one divide by three))
sin2(x)/(x(1/3))
sin2x/x1/3
sin²(x)/(x^(1/3))
sin to the power of 2(x)/(x to the power of (1/3))
sin^2x/x^1/3
sin^2(x) divide by (x^(1 divide by 3))

Sum of series sin^2(x)/(x^(1/3))

You have entered [src]

  oo         
____         
\   `        
 \       2   
  \   sin (x)
   )  -------
  /    3 ___ 
 /     \/ x  
/___,        
n = 1

\sum_{n=1}^{\infty} \frac{\sin^{2}{\left(x \right)}}{\sqrt[3]{x}}

Sum(sin(x)^2/x^(1/3), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{\sin^{2}{\left(x \right)}}{\sqrt[3]{x}}

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{\sin^{2}{\left(x \right)}}{\sqrt[3]{x}}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

      2   
oo*sin (x)
----------
  3 ___   
  \/ x

\frac{\infty \sin^{2}{\left(x \right)}}{\sqrt[3]{x}}

oo*sin(x)^2/x^(1/3)