Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
- Differential equations Step by Step
- Product of series
-
How to use it?
- Sum of series:
- n^2*x^(n-1)
-
(2*n-3)/(n^2+2)
-
n^2/e^(sqrt(n))
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ln((n^3-1)/(n^3+1))
- Derivative of:
- n^2*x^(n-1)
-
Identical expressions
- n^ two *x^(n- one)
- n squared multiply by x to the power of (n minus 1)
- n to the power of two multiply by x to the power of (n minus one)
- n2*x(n-1)
- n2*xn-1
- n²*x^(n-1)
- n to the power of 2*x to the power of (n-1)
- n^2x^(n-1)
- n2x(n-1)
- n2xn-1
- n^2x^n-1
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Similar expressions
- n^2*x^(n+1)
Sum of series n^2*x^(n-1)
The solution
You have entered
[src]
oo ___ \ ` \ 2 n - 1 / n *x /__, n = 1
$$\sum_{n=1}^{\infty} n^{2} x^{n - 1}$$
Sum(n^2*x^(n - 1), (n, 1, oo))
The answer
[src]
/x*(-1 - x)
|---------- for |x| < 1
| 3
|(-1 + x)
|
| oo
< ___
| \ `
| \ 2 n
| / n *x otherwise
| /__,
|n = 1
\
-------------------------
x
$$\frac{\begin{cases} \frac{x \left(- x - 1\right)}{\left(x - 1\right)^{3}} & \text{for}\: \left|{x}\right| < 1 \\\sum_{n=1}^{\infty} n^{2} x^{n} & \text{otherwise} \end{cases}}{x}$$
Piecewise((x*(-1 - x)/(-1 + x)^3, |x| < 1), (Sum(n^2*x^n, (n, 1, oo)), True))/x
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