Mister Exam

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Sum of series:
(-1)^n*(2*2)^(2*n)/factorial(2*n)
k^2
log(n+1)/(n+1)
sin((n+1)/(2*n-1))^2
Identical expressions
six , fourteen *(forty +n)
6,14 multiply by (40 plus n)
six , fourteen multiply by (forty plus n)
6,14(40+n)
6,1440+n
Similar expressions
6,14*(40-n)

Sum of series/ 6,14*(40+n)

Sum of series 6,14*(40+n)

The solution

You have entered [src]

 400              
 ___              
 \  `             
  \   307*(40 + n)
   )  ------------
  /        50     
 /__,             
n = 1

\sum_{n=1}^{400} \frac{307 \left(n + 40\right)}{50}

Sum(307*(40 + n)/50, (n, 1, 400))

The rate of convergence of the power series

The answer [src]

590668

Numerical answer [src]

590668.000000000000000000000000

590668.000000000000000000000000

The graph

Sum of series 6,14*(40+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
```