Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 162

Study the convergence of the series $sum_{n ge 1} sin frac{1}{n^{5/4}}$.

I have to show whether the series $$sum_{n ge 1}sin frac{1}{n^{5/4}}$$ is convergent or not. This is what I tried, but I am not sure if it's correct: We...

Asked on 12/31/2020 by user592938

1 answer

Cycle-tree order relation

I am trying to express a cycle-tree structure (https://math.stackexchange.com/a/3835246/427611) as an ordered set. I want to extend the notion of a cycle-tree structure onto continuous structures as well. Here...

Asked on 12/31/2020 by Alex C

0 answer

Triple Integrals Find the mass of the solid S made out of material with density f.

Find the mass of the solid S made out of material with density f in maple.S is a ball bounded by the sphere (x−2)^2+(y+3)^2+(z−4)^2 =5; f(x, y, z)=x^2y^2. How...

Asked on 12/31/2020 by Buddy

1 answer

Find numbers $a_n$ such that $a_n > a_{n+1}$ and $a_n, a_{n+1}$ that satisfies the inequality $a_n geq frac{1}{(n+1)^2} + a_{n+1}$

I'm working on a project for my introduction to abstract math course and I'm stuck on a particular part of it. We're supposed to prove $sum_{k=1}^{n} frac{1}{k^2} < frac{7}{4}$...

Asked on 12/31/2020 by Calypso Rivers

1 answer

General solution of an ODE from the general solution of a PDE/SDE/SPDE and most general "differential" equation

Is it possible to obtain the general solution of an ODE by solving a PDE, SDE or SPDE? I haven't dived into PDEs, nor SDEs, therefore the question. Another question...

Asked on 12/30/2020 by Andrés M. Santos Ramírez

0 answer

Proving there is a constant $C$ such that $f=g+C$

Consider the following lemma:Lemma: Let $f:[a,b]tomathbb{R}$ continuous on $[a,b]$ and differentiable on $(a,b)$, If $f'(x)=0$ for all $xin [a,b]$, then $f$ is constant on...

Asked on 12/30/2020 by user926356

0 answer

Show that the density is $f(x)=frac{e^{-x}}{left(1+e^{-x}right)^{2}}$

A positive random variable $X$ has the logistic distribution if its distribution function is given by$$F(x)=P(X leq x)=frac{1}{1+e^{-(x-mu) / beta}} ; quad(x>0)$$for parameters ...

Asked on 12/30/2020

0 answer

Is the function injective if the Jacobian has full column rank?

Let $f:mathbb{R}^m to mathbb{R}^n: x to f(x)$ be a continuous and differentiable function with $m < n$. If the Jacobian $J_f$ has full column rank (i.e., rank=...

Asked on 12/30/2020 by Abdul Fatir

1 answer

Can't find n (algebraic manipulation)

I‘m trying to understand a proof on my textbook that says $sqrt {n − 1} +sqrt {n + 1}$ is irrational, where $n in mathbb{N} $. However I...

Asked on 12/30/2020 by Heng Wei

2 answer

Calculating probability of getting at least 3 red ball drawn from a bag having 6 red ball,5 blue,4 green in 5th attempt.

There are 6 red balls,5 blue balls,and 4 green balls in a bag. What is the probability of drawing at least 3 red ball in 5th attempt. Assume balls are...

Asked on 12/30/2020 by Rajakr

1 answer

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