Mister Exam

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Sum of series:
a^n
5/(25*n^2-5*n-6)
(2^x+3^x)/6^x
sqrt(n)/(n^p+1)
Identical expressions
sqrt(n)/(n^p+ one)
square root of (n) divide by (n to the power of p plus 1)
square root of (n) divide by (n to the power of p plus one)
√(n)/(n^p+1)
sqrt(n)/(np+1)
sqrtn/np+1
sqrtn/n^p+1
sqrt(n) divide by (n^p+1)
Similar expressions
sqrt(n)/(n^p-1)

Sum of series/ sqrt(n)/(n^p+1)

Sum of series sqrt(n)/(n^p+1)

The solution

You have entered [src]

  oo        
____        
\   `       
 \      ___ 
  \   \/ n  
   )  ------
  /    p    
 /    n  + 1
/___,       
n = 1

\sum_{n=1}^{\infty} \frac{\sqrt{n}}{n^{p} + 1}

Sum(sqrt(n)/(n^p + 1), (n, 1, oo))

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```