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  • Sum of series:
  • 1/(3n-2)*(3n+1) 1/(3n-2)*(3n+1)
  • 2/n 2/n
  • n^2*x^(n-1)
  • 1/n^1,5 1/n^1,5
  • Derivative of:
  • n^2*x^(n-1)

  • Identical expressions

  • n^ two *x^(n- one)
  • n squared multiply by x to the power of (n minus 1)
  • n to the power of two multiply by x to the power of (n minus one)
  • n2*x(n-1)
  • n2*xn-1
  • n²*x^(n-1)
  • n to the power of 2*x to the power of (n-1)
  • n^2x^(n-1)
  • n2x(n-1)
  • n2xn-1
  • n^2x^n-1

  • Similar expressions

  • n^2*x^(n+1)
Sum of series/ n^2*x^(n-1)

Sum of series n^2*x^(n-1)


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The solution

You have entered [src] 
  oo           
 ___           
 \  `          
  \    2  n - 1
  /   n *x     
 /__,          
n = 1
$$\sum_{n=1}^{\infty} n^{2} x^{n - 1}$$ 
Sum(n^2*x^(n - 1), (n, 1, oo))
The answer [src] 
/x*(-1 - x)              
|----------   for |x| < 1
|        3               
|(-1 + x)                
|                        
|  oo                    
< ___                    
| \  `                   
|  \    2  n             
|  /   n *x    otherwise 
| /__,                   
|n = 1                   
\                        
-------------------------
            x
$$\frac{\begin{cases} \frac{x \left(- x - 1\right)}{\left(x - 1\right)^{3}} & \text{for}\: \left|{x}\right| < 1 \\\sum_{n=1}^{\infty} n^{2} x^{n} & \text{otherwise} \end{cases}}{x}$$ 
Piecewise((x*(-1 - x)/(-1 + x)^3, |x| < 1), (Sum(n^2*x^n, (n, 1, oo)), True))/x

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