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  • Sum of series:
  • tg^(2)*(6/(2n)^(1/3))*(x-24)^n
  • (4*9^n-2^n)/18^n (4*9^n-2^n)/18^n
  • 1/((3*n+1)*(3*n+4)) 1/((3*n+1)*(3*n+4))
  • 1/(2*n-1)*(2*n+1) 1/(2*n-1)*(2*n+1)

  • Identical expressions

  • sqrt(n)*(x+ three)^n/n^ two + one
  • square root of (n) multiply by (x plus 3) to the power of n divide by n squared plus 1
  • square root of (n) multiply by (x plus three) to the power of n divide by n to the power of two plus one
  • √(n)*(x+3)^n/n^2+1
  • sqrt(n)*(x+3)n/n2+1
  • sqrtn*x+3n/n2+1
  • sqrt(n)*(x+3)^n/n²+1
  • sqrt(n)*(x+3) to the power of n/n to the power of 2+1
  • sqrt(n)(x+3)^n/n^2+1
  • sqrt(n)(x+3)n/n2+1
  • sqrtnx+3n/n2+1
  • sqrtnx+3^n/n^2+1
  • sqrt(n)*(x+3)^n divide by n^2+1

  • Similar expressions

  • sqrt(n)*(x-3)^n/n^2+1
  • sqrt(n)*(x+3)^n/n^2-1
Sum of series/ sqrt(n)*(x+3)^n/n^2+1

Sum of series sqrt(n)*(x+3)^n/n^2+1


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The solution

You have entered [src] 
  oo                      
____                      
\   `                     
 \    /  ___        n    \
  \   |\/ n *(x + 3)     |
   )  |-------------- + 1|
  /   |       2          |
 /    \      n           /
/___,                     
n = 1
$$\sum_{n=1}^{\infty} \left(1 + \frac{\sqrt{n} \left(x + 3\right)^{n}}{n^{2}}\right)$$ 
Sum((sqrt(n)*(x + 3)^n)/n^2 + 1, (n, 1, oo))
The answer [src] 
  oo                
____                
\   `               
 \    /           n\
  \   |    (3 + x) |
   )  |1 + --------|
  /   |       3/2  |
 /    \      n     /
/___,               
n = 1
$$\sum_{n=1}^{\infty} \left(1 + \frac{\left(x + 3\right)^{n}}{n^{\frac{3}{2}}}\right)$$ 
Sum(1 + (3 + x)^n/n^(3/2), (n, 1, oo))

    Examples of finding the sum of a series

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