Mister Exam

Lang:

Other calculators

n*(arcsin(1/n))^n

How to use it?
Sum of series:
1/((4n-3)(4n+1))
3/n
sen(ix)
(3*k-5)*(3*k+6)-(3*k-11)*(3*k+12)
Identical expressions
n*(arcsin(one /n))^n
n multiply by (arc sinus of (1 divide by n)) to the power of n
n multiply by (arc sinus of (one divide by n)) to the power of n
n*(arcsin(1/n))n
n*arcsin1/nn
n(arcsin(1/n))^n
n(arcsin(1/n))n
narcsin1/nn
narcsin1/n^n
n*(arcsin(1 divide by n))^n

Sum of series/ n*(arcsin(1/n))^n

Sum of series n*(arcsin(1/n))^n

The solution

You have entered [src]

  oo            
 ___            
 \  `           
  \         n/1\
   )  n*asin |-|
  /          \n/
 /__,           
n = 1

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

Sum(n*asin(1/n)^n, (n, 1, oo))

The rate of convergence of the power series

Numerical answer [src]

2.25495253951805932524950787259

2.25495253951805932524950787259

The graph

Sum of series n*(arcsin(1/n))^n

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
```