Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
- Differential equations Step by Step
- Product of series
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How to use it?
- Sum of series:
- 2/(x^2+2x)
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1,65
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sin(sin(n)/n^(1/3))
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6/(9*n^2+12*n-5)
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Identical expressions
- arctg(n(one +(- one ^n))/ two)/(n^ three + two)
- arctg(n(1 plus ( minus 1 to the power of n)) divide by 2) divide by (n cubed plus 2)
- arctg(n(one plus ( minus one to the power of n)) divide by two) divide by (n to the power of three plus two)
- arctg(n(1+(-1n))/2)/(n3+2)
- arctgn1+-1n/2/n3+2
- arctg(n(1+(-1^n))/2)/(n³+2)
- arctg(n(1+(-1 to the power of n))/2)/(n to the power of 3+2)
- arctgn1+-1^n/2/n^3+2
- arctg(n(1+(-1^n)) divide by 2) divide by (n^3+2)
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Similar expressions
- arctg(n(1-(-1^n))/2)/(n^3+2)
- arctg(n(1+(-1^n))/2)/(n^3-2)
- arctg(n(1+(1^n))/2)/(n^3+2)
Sum of series arctg(n(1+(-1^n))/2)/(n^3+2)
The solution
You have entered
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\ `
\ / / n\\
\ |n*\1 - 1 /|
\ atan|----------|
) \ 2 /
/ ----------------
/ 3
/ n + 2
/____,
n = 1
$$\sum_{n=1}^{\infty} \frac{\operatorname{atan}{\left(\frac{n \left(1 - 1^{n}\right)}{2} \right)}}{n^{3} + 2}$$
Sum(atan((n*(1 - 1^n))/2)/(n^3 + 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