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:
- nx^n!
-
(937/40-307/10)^2/18
- x^n/(√(n+1)*4n)
- x^factorial(n)
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Identical expressions
- x*(one +k)^(n- one)
- x multiply by (1 plus k) to the power of (n minus 1)
- x multiply by (one plus k) to the power of (n minus one)
- x*(1+k)(n-1)
- x*1+kn-1
- x(1+k)^(n-1)
- x(1+k)(n-1)
- x1+kn-1
- x1+k^n-1
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Similar expressions
- x*(1-k)^(n-1)
- x*(1+k)^(n+1)
Sum of series x*(1+k)^(n-1)
The solution
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[src]
12 ___ \ ` \ n - 1 / x*(1 + k) /__, n = 1
$$\sum_{n=1}^{12} x \left(k + 1\right)^{n - 1}$$
Sum(x*(1 + k)^(n - 1), (n, 1, 12))
The answer
[src]
/ 2 3 4 5 6 7 8 9 10 11\ x*\2 + k + (1 + k) + (1 + k) + (1 + k) + (1 + k) + (1 + k) + (1 + k) + (1 + k) + (1 + k) + (1 + k) + (1 + k) /
$$x \left(k + \left(k + 1\right)^{11} + \left(k + 1\right)^{10} + \left(k + 1\right)^{9} + \left(k + 1\right)^{8} + \left(k + 1\right)^{7} + \left(k + 1\right)^{6} + \left(k + 1\right)^{5} + \left(k + 1\right)^{4} + \left(k + 1\right)^{3} + \left(k + 1\right)^{2} + 2\right)$$
x*(2 + k + (1 + k)^2 + (1 + k)^3 + (1 + k)^4 + (1 + k)^5 + (1 + k)^6 + (1 + k)^7 + (1 + k)^8 + (1 + k)^9 + (1 + k)^10 + (1 + k)^11)
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