Mister Exam

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How to use it?
Sum of series:
sqrt((n+4)/((n^4)+4))
pi^(-n)/pi^n
6/((3*n-1)*(3*n+5))
cosnx/(nsqrtn)
Identical expressions
sin^ two (xn)
sinus of squared (xn)
sinus of to the power of two (xn)
sin2(xn)
sin2xn
sin²(xn)
sin to the power of 2(xn)
sin^2xn

Sum of series sin^2(xn)

The solution

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  6           
 ___          
 \  `         
  \      2/ n\
  /   sin \x /
 /__,         
n = 1

$$\sum_{n=1}^{6} \sin^{2}{\left(x^{n} \right)}$$

Sum(sin(x^n)^2, (n, 1, 6))

The answer [src]

   2         2/ 2\      2/ 3\      2/ 4\      2/ 5\      2/ 6\
sin (x) + sin \x / + sin \x / + sin \x / + sin \x / + sin \x /

$$\sin^{2}{\left(x \right)} + \sin^{2}{\left(x^{2} \right)} + \sin^{2}{\left(x^{3} \right)} + \sin^{2}{\left(x^{4} \right)} + \sin^{2}{\left(x^{5} \right)} + \sin^{2}{\left(x^{6} \right)}$$

sin(x)^2 + sin(x^2)^2 + sin(x^3)^2 + sin(x^4)^2 + sin(x^5)^2 + sin(x^6)^2

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

Sum of series sin^2(xn)

The solution

Examples of finding the sum of a series