Mister Exam

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Sum of series:
7/(49n^2-70n-24)
1/2^(2n-2)
|(1/(n)^(1/2)-1/(n+1))|^3
x²-16
Identical expressions
(one -sin(nx))/n^ two
(1 minus sinus of (nx)) divide by n squared
(one minus sinus of (nx)) divide by n to the power of two
(1-sin(nx))/n2
1-sinnx/n2
(1-sin(nx))/n²
(1-sin(nx))/n to the power of 2
1-sinnx/n^2
(1-sin(nx)) divide by n^2
Similar expressions
(1+sin(nx))/n^2

Sum of series (1-sin(nx))/n^2

The solution

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  oo              
____              
\   `             
 \    1 - sin(n*x)
  \   ------------
  /         2     
 /         n      
/___,             
n = 1

$$\sum_{n=1}^{\infty} \frac{1 - \sin{\left(n x \right)}}{n^{2}}$$

Sum((1 - sin(n*x))/n^2, (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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series (1-sin(nx))/n^2

The solution

Examples of finding the sum of a series