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

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:
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 ...
• 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 ...