Mister Exam

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Sum of series:
sin^2((n^2+3)/(n^3+2))
ln(n)/n^1.01-1/n^1.01
1/((2n-1)(2n)(2n+1))
sin(1/k)
Identical expressions
sin^ two ((n^ two + three)/(n^ three + two))
sinus of squared ((n squared plus 3) divide by (n cubed plus 2))
sinus of to the power of two ((n to the power of two plus three) divide by (n to the power of three plus two))
sin2((n2+3)/(n3+2))
sin2n2+3/n3+2
sin²((n²+3)/(n³+2))
sin to the power of 2((n to the power of 2+3)/(n to the power of 3+2))
sin^2n^2+3/n^3+2
sin^2((n^2+3) divide by (n^3+2))
Similar expressions
sin^2((n^2+3)/(n^3-2))
sin^2((n^2-3)/(n^3+2))

Sum of series/ sin^2((n^2+3)/(n^3+2))

Sum of series sin^2((n^2+3)/(n^3+2))

The solution

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  oo              
____              
\   `             
 \        / 2    \
  \      2|n  + 3|
   )  sin |------|
  /       | 3    |
 /        \n  + 2/
/___,             
n = 1

$$\sum_{n=1}^{\infty} \sin^{2}{\left(\frac{n^{2} + 3}{n^{3} + 2} \right)}$$

Sum(sin((n^2 + 3)/(n^3 + 2))^2, (n, 1, oo))

The rate of convergence of the power series

The graph

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
```

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Identical expressions

Similar expressions

Sum of series sin^2((n^2+3)/(n^3+2))

The solution

Examples of finding the sum of a series