Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 6

A sequence $f_n to f$ uniformly on $(0,1)$ where $f, f_n in C([0,1])$ implies $f_n(0) to f(0)$, $f_n(1) to f(1)$.

This is a past problem for an Applied Math QR Exam:Suppose $f_n$, for $n in mathbb{N}$, and $f$ arecontinuous functions on the closed interval $[0,1]$....

Asked on 01/05/2022 by CyCeez

0 answer

Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimension

I don't know what to do with the following question:Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimensionSupposedly it's...

Asked on 01/05/2022

1 answer

Can $a bmod 3$ be represented arithmetically without the mod or other integer-related functions?

I've noticed that $a bmod b$ (with 'mod' in the operational sense) can also be represented using various tricks of formulation. For instance, that $$a bmod b =...

Asked on 01/05/2022

2 answer

When is $sum_{i=1}^{m}i^n =0 bmod dfrac{m(m+1)}{2}$?

I have tried to creat such formula related to divisibility using triangulair numbers and series , I have got the following problem such that I ask when is ...

Asked on 01/05/2022

0 answer

My proof of $A^{mathrm{c}}$ is closed iff $A$ is open

$newcommand{c}{mathrm{c}}$ I have already attempted the proof but I feel like there are some holes in my argument. if someone could look at it and point it out even...

Asked on 01/05/2022 by mathematicaxyz

1 answer

Define $X_n=sum_{k=1}^n kx_k$ and $Y_n=sum_{k=1}^n ky_k$. Prove that there exists an $n$ such that $X_n<Y_n$.

Question: Let $x_k, y_kgeq 0$. Suppose that $sum_{k=1}^infty x_k<infty$ and $sum_{k=1}^infty y_k=infty$. Define $X_n=sum_{k=1}^n kx_k$ and $Y_n=sum_{k=1}^n ky_k$. Prove that there exists...

Asked on 01/05/2022

2 answer

Find the values of $k$ that satisfy $gcd(a,b)=5$

Let $a$,$b$ and $k$ be integers such that$$a=6k+4$$$$b=11k+4$$Find $k$ values that satisfy $gcd(a,b)=5$ Note: $(a,b)$ are solutions to the...

Asked on 01/05/2022 by ricin

2 answer

How find the solution to $ sum_{i=1}^{infty} left( frac{1}{2} right)^i left( frac{1}{i}right)$?

I am having trouble trying to figure out the solution to the infinite series $ sum_{i=1}^{infty} left( frac{1}{2} right)^i left( frac{1}{i}right)$. What kind of infinite series is this, and...

Asked on 01/05/2022

2 answer

Closed form for the maximum of the two-variable function $(a x + (1 - a) y) (b (1 - x) + (1 - b) (1 - y))$

I'm trying to characterize the maximum of this function within the unit interval ($x,yin [0,1]$): $$f(x,y)=(a x + (1 - a) y) (b (1 - x) + (1...

Asked on 01/05/2022

0 answer

Interesting connection between a word problem and a physics formula

I came across a math word problem about the time it takes workers to finish a job when they're together vs. separately and I found its connection to a formula...

Asked on 01/05/2022

0 answer

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