## How to prove the identity $\sum_{n=1}^{\infty} \dfrac{{H_{n}}^2}{n^2} = \dfrac{17}{360} {\pi}^4$ February 14

Prove That $$\sum_{n=1}^{\infty} \dfrac{{H_{n}}^2}{n^2} = \dfrac{17}{360} {\pi}^4$$ I encountered this identity while reading the article about Harmonic Number on Wikipedia. I thought of using the integral representation of Harmonic Number, but the s

## Show given relation R is equivalence relation on S February 14

I will display the exact problem, then my questions. I have searched to the extremes to figure this out and can't:Show that the tgiven relation R is an equivalence relation on set S. S is the set of ordered pairs of positive integers. Define R so tha

## Derivative of Integral -2tt, with upper limit of x^2 February 14

F(x)= ∫(-2t-2)dt, with the lower limit x and upper limit x^2. F'(X) should be simple, and just be (-2(x^2) - 2)* 2x, which equals -4x^3 - 4x.However, for some reason, the worksheet says the answer should be -4x^3 -2x + 2.Number 6, here: http://cdn.ku

## Why if $\lim_{n \rightarrow \infty} f_n(x)=f(x)$ for all $x \in X$, we cannot directly say that $f(x)$ is the uniform limit of $f_n(x)$ as well February 14

I'm trying to understand why if, given $f_n(x)$ with $x \in X$ and $\lim_{n \rightarrow \infty} f_n(x)=f(x)$ for all $x \in X$, we cannot directly say that $f(x)$ is the uniform limit of $f_n(x)$. Can you confirm me that the reason is that according

## can you consider a series to be a sequence of sums February 14    1

for examplesequence: $1/(2^n), \qquad n\ge 0$sequence for the series: $1, 1.5, 1.75, 1.875, \ldots$and if so, does that mean you can use/extend sequence theorems for series?Yes in fact that is what a series is considered to be. When you ask about con

## Calculating a growing series in Spreadsheet February 14    1

I've got a spreadsheet, where I'm trying to calculate the amount of retained users over time for a subscription based service. https://docs.google.com/spreadsheet/ccc?key=0ArE8l42n3soadGJGRmtZMWdpeFZKSTQycEtKRXE5ZFE#gid=0I can get the totals but it's

## How do you derive a function that describes a series February 14    2

It's been a really long time since I've done calculus or any other kind of math beyond tip calculation. I was given a spreadsheet that calculates and plots a growth curve over time based on a handful of inputs. It goes out for one year. I'd like to b

## Cartesian Product converted into Summation February 14

I am looking at the proof of Maximum Likelihood Estimator and So let's get to it: first take the $\log$ of the equation: $$\log(P(\text{DATA}))=\log\prod i=1N(PX_i(1−P)1−X_i)$$Since $$\log(a b)=\log(a)+\log(b)$$then all the terms of the product becom

## The exact binomial test formula February 14    2

Could you help me find the one-sided exact binomial test formula?I use this statistical test in R-language, but I can't find the formula for it.Eng Wikipedia (https://en.wikipedia.org/wiki/Binomial_test) and RLang help gives me only examples without

## Inverse Gaussian, Limiting Distributions February 14    1

I'm trying to understand the nature of limiting distributions and distributions, specifically$1/Z_n \longrightarrow ~?$ where $Z_n\longrightarrow Z -Gaussian(0,1)$I understand that the gamma distribution converges to the gaussian for a large enough $You Might Also Like • I need some help! Thank you in advance.Let K$^{n*n}$& M$^{n*n}$be two square matrices, and K$\cdot$M=\ ... • How should I solve this second order, nonlinear ODE?: $$\left(\frac{f''(x)}{B}\right)^n=-(f(x)-a_0-a_1x-\cdo ... • I have these two definitions of span:Span: Su ... • Suppose U = \{(x, y, x+y, x -y, 2x) \in \Bbb F^5 : x, y \in \Bbb F\}. Find three subspaces W_1, W_2, W_3 ... • It would be helpful if I can get some comparison between these three books,T. Tao, An epsilon of room, I, Gr ... • In H. S. Wilf's generatingfunctionology, (1.6.8) describes:$$ A_n(y) = \sum_k \begin{Bmatrix}n-1\\k-1\end{Bm ... • I've been told that strong induction and weak induction are equivalent. However, in all of the proofs I've s ... • Please forgive my lack of maths knowledge,It is my understanding that:Standard Deviation is the average dist ... • Prove$x^{2 \over 3} \ln(x)$is uniformly continuous in$(1,\infty)$To my understanding I need to show the d ... • I have the following integral involving a confluent hypergeometric function:$\$\int_{0}^{\infty}x^3e^{-ax^2}{ ...