Mister Exam

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Sum of series:
(2^n+(-1)^n)/5^n
1/(4n^2-1)
(n+1)/n
(3^n-2^n)/6^n
Identical expressions
n/sqrt(arcsin(pi/(n+ one)))
n divide by square root of (arc sinus of ( Pi divide by (n plus 1)))
n divide by square root of (arc sinus of ( Pi divide by (n plus one)))
n/√(arcsin(pi/(n+1)))
n/sqrtarcsinpi/n+1
n divide by sqrt(arcsin(pi divide by (n+1)))
Similar expressions
n/sqrt(arcsin(pi/(n-1)))

Sum of series n/sqrt(arcsin(pi/(n+1)))

The solution

You have entered [src]

  oo                    
_____                   
\    `                  
 \             n        
  \    -----------------
   \       _____________
   /      /     /  pi \ 
  /      /  asin|-----| 
 /     \/       \n + 1/ 
/____,                  
n = 1

$$\sum_{n=1}^{\infty} \frac{n}{\sqrt{\operatorname{asin}{\left(\frac{\pi}{n + 1} \right)}}}$$

Sum(n/sqrt(asin(pi/(n + 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
```

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How to use it?

Identical expressions

Similar expressions

Sum of series n/sqrt(arcsin(pi/(n+1)))

The solution

Examples of finding the sum of a series