Скачать или смотреть Solving Berkley math competition question. Sum k^2/2^k , k from 1 to infinity.

Solving Berkley math competition question. Try it yourself. Find the above sum. Sum of k^2/2^k from 1 to infinity.
$\sum_{ k=1 }^{\infty}\frac(k^2)(2^k)$
We will the famous series 1/(1-x) to find the sum by using techniques of diffferentiations.

How to differentiate a series. How to get the sum from the differentiation of a series? What is the radius of convergence? What's the interval of convergence? How to find the sum of the series by using differential equations or techniques of the sum? So here, in this case, we're going to have to find the sum of the series. We're gonna use the series 1 over 1. Minus X Fine. It's derivative twice. And after that, we're gonna use some specific values to plug in and find the sum note here that we are assuming that the series is convergent and therefore, it's derivative of the first kind it's derivative. The second one is also conversant and they have the same radius of convergence. In our case here, we're gonna use what we know about series like differentiation and integration and also the radius of convergence to try to find the sum. This question is coming from Berkeley math competition so it's very good question and we now to how to solve it, please try it yourself. This question is helpful for students trying to get their teacher licensure for student, taking math, practice 5161, And it's also for students trying to do competitions, like Stanford competition, Harvard competition Berkeley math, compassion, competition, Princeton Matt, competition, and all the classes, and for grad, students, and students taking MIT courses. This one can be very helpful for them to learn about series and how to find the sums in some special cases. #maths #olympiad #education #calculus #mit #chemistry #python #physics #howtosolveolympiadmathproblem