Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 69

Is this series $sum_{n=0}^{infty} 2^{(-1)^n - n} = 3 $ or $ approx 3$

Is this series $sum_{n=0}^{infty} 2^{(-1)^n - n} = 3 $ or $ approx 3$ Hello all.In Ross' elementary Analysis Chapter 14 there is an example of the...

Asked on 11/24/2021

2 answer

Does the Riemannian distance function obey the Leibniz rule?

Let $M$ be a Riemannian manifold, and let $alpha,beta:[0,delta) to M$ be two smooth paths satisfying $alpha(t) neq beta(t)$ for every $t$. Suppose that for...

Asked on 11/24/2021 by Asaf Shachar

1 answer

Non Case Analysis Proof of Triangle Inequality for Hamming Distance

I've written a proof for the triangle inequality for the Hamming distance metric on ordered triplets of ones and zeroes. I wanted to try to come up with a proof...

Asked on 11/24/2021 by Henry Powell

1 answer

A non-circular argument that uses the Maclaurin series expansions of $sin x$ and $cos x$ to show that $frac{d}{dx}sin x = cos x$

I have often heard it said that it is circular to use the Maclaurin series expansions of sine and cosine to show that $frac{d}{dx}sin x = cos x$ because...

Asked on 11/24/2021

1 answer

$|int_a^b f(x)dx| leq |int_a^b |f(x)| dx| $?

For $a>b$ Does the following hold: $|int_a^b f(x)dx| leq |int_a^b |f(x)| dx| $ ? At $"leq"$ I have used the triangular inequality for integrals: If $f:Ito...

Asked on 11/24/2021

1 answer

Number of permutations of the letters $a, b, c, d$ such that $b$ does not follow $a$, and $c$ does not follow $b$, and $d$ does not follow $c$

QUESTION: Find the number of permutations of the letters $a, b, c, d$ such that ...

Asked on 11/24/2021

2 answer

Diagonalizability of an operator

Given $T:Vto V$ a linear operator, such that $m_{T}=(x-c_{1})^{r_{1}}...(x-c_{k})^{r_{k}}, ineq jto c_{i}neq c_{j}$, we'll denote for each $i$, $E_{i}$ is the projection onto $Ker((T-c_{i})^{r_{i}})$, with...

Asked on 11/24/2021 by GBA

1 answer

What is the probability for $x$ to be positive only?

If $x,y,zin mathbb R$ and $x+y+z=5,, xy+yz+zx=3$, what is the probability that $x>0$ ? $$(a)quadfrac3{16}qquad (b)quadfrac5{16}qquad (c)quadfrac{13}{16}qquad (d)quad frac{15}{16}$$ I've tried forming a cubic equation and...

Asked on 11/24/2021 by amateurashish

2 answer

A simple proof of Sylow theorem for abelian groups

In my attempt to proveLet $G$ be an abelian group and $H,K$ its subgroups such that $o(H) = m$ and $o(K) = n$. Then $G$...

Asked on 11/24/2021

1 answer

Question about the proof of the index theorem appearing in Milnor's Morse Theory

I am trying to get through the proof of the index theorem. The background: I have been stuck for quite a while on the following point which Milnor says is...

Asked on 11/24/2021 by doggerel

1 answer

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