Mister Exam

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Sum of series:
38
arctan(n)/(n!)^2
arctg(5/n)/n!
ln((n^2+n+3)/(n^2+n+2))
Identical expressions
one , five * forty-one , sixty-eight
1,5 multiply by 41,68
one , five multiply by forty minus one , sixty minus eight
1,541,68

Sum of series/ 1,5*41,68

Sum of series 1,5*41,68

The solution

You have entered [src]

  3         
 ___        
 \  `       
  \   3*1042
   )  ------
  /    2*25 
 /__,       
n = 1

$$\sum_{n=1}^{3} \frac{3 \cdot 1042}{2 \cdot 25}$$

Sum(3*1042/(2*25), (n, 1, 3))

The rate of convergence of the power series

The answer [src]

4689
----
 25

$$\frac{4689}{25}$$

4689/25

Numerical answer [src]

187.560000000000000000000000000

187.560000000000000000000000000

The graph

Sum of series 1,5*41,68

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
```