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How do I calculate the infinite sum of this series? $$\\sum_{n=1}^{\\infty}n^2q^n = -\\frac{q(q+1)}{(q-1)^3}\\ \\text{when}\\ |q| < 1.$$ How does wolfram alpha get ...

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Wolfram Community forum discussion about Calculate the sum of an infinite series?. Stay on top of important topics and build connections by joining Wolfram Community groups relevant to your interests.
Quaternion Result. One approach might be to define a quaternion which, when multiplied by a vector, rotates it: p 2 =q * p 1. This almost works as explained on this page.. However, to rotate a vector, we must use this formula:
Infinite Series Calculator. Sum of: ... Build your own widget » Browse widget gallery » Learn more » Report a problem » Powered by Wolfram|Alpha Terms ...
2) Notice that the coefficient of x is the sum of two numbers ( the roots) and the constant is the product of two numbers 3) Now make the connection with your problem! We want a+b= -23 and ab=132 for integer a and b, so substitute into the equation in 1) to obtain the quadratic x^2+23x+132 with roots x=a and x=b.
Infinite Series: Root Test For Convergence The root test may be used to test for convergence of an infinite series.
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. ... Assuming "infinite sum" refers to a computation ... Use as a general topic instead. Computational Inputs: Assuming sum convergence calculator | Use sum calculator instead » summand ...
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Many observations of the greatest number in a sample of size drawn randomly from the specified distribution are taken and displayed via a histogram Get the free Taylor Series Calculator widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha . Mathematica in the Wolfram Product Universe.
This formula reflects the definition of the convergent infinite sums (series) . The sum converges absolutely if . If this series can converge conditionally; for example, converges conditionally if , and absolutely for . If , the series does not converge (it is a divergent series).
  • Nov 29, 2009 · It’s awesome. Wolfram has more capability though- residue calculation, infinite sums, factoring/solving/etc when you have constants like ax 2+4x=0. Wolfram can be spotty with copying and pasting TeX though. I usually use a combination of both! Symbolab for simpler things like matrix multiplication and Wolfram for more complicated things like ...
  • This calculator will find the infinite sum of arithmetic, geometric, power, and binomial series, as well as the partial sum, with steps shown (if possible). It will also check whether the series converges.
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  • Jun 24, 2010 · I plugged what I got into Wolfram Alpha & got an astonishingly simple equation: s^2/6 * sqrt (12l^2-s^2). Since the volume of the pyramid comprises half the volume of the trigonal antiprism, the equation for an oblique rectangular pyramid is s^2/12 * sqrt (12l^2-s^2).
  • Free series convergence calculator - test infinite series for convergence step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy.
  • Nov 05, 2020 · Power Series Calculator is a free online tool that displays the infinite series of the given function. Jquery Post Headers Example, We also use third-party cookies that help us analyze and understand how you use this website.
  • How do I calculate the infinite sum of this series? $$\sum_{n=1}^{\infty}n^2q^n = -\frac{q(q+1)}{(q-1)^3}\ \text{when}\ |q| < 1.$$ How does wolfram alpha get this result? Stack Exchange Network. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to ...
  • These are the functions of the form Sum[p[k,x] Exp[a x],{k,1,n}] where p[k,x] are polynomials in x, and a is complex, or correspondingly sums with sines and cosines. Further the package is able to convert this procedure, i.e. to calculate the generating function of a sequence.
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