Zarrax
Reputation
31,023
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# 1,717 Actions

 Apr 28 answered $1\le p \lt \infty$ and $f_k$ nonnegative increasing. Then $f_k\to f$ in $L_p$ iff $\sup_k||f_k||_p \lt \infty$. Apr 24 comment Simplify vector equation $2\mathbf c - (\mathbf a + \mathbf b)\times(\mathbf a - \mathbf b)$ in addition, the answer will depend on whether ${\bf c}$ is in the direction of ${\bf a \times b}$ or ${\bf b \times a}$ Apr 24 comment Show : $\displaystyle \sum_{n=1}^\infty \dfrac{a_n}{1+a_n}$ is absolutely convergent It's right, except you should put everything in absolute values, since the limit comparison test applies only to series with nonnegative terms. Apr 24 answered Show : $\displaystyle \sum_{n=1}^\infty \dfrac{a_n}{1+a_n}$ is absolutely convergent Mar 31 answered Does the Series $\sum_{n=1}^{\infty} (1-\cos\frac{\pi}{n})$ Converge? Mar 20 comment Prove that $|a|+|b|+|c|\le17$ if $|ax^2+bx+c|\le1$ for $0\le x\le1$ If the second derivative of a function is constant on some interval, you can bound the maximum of this function's absolute value from below in terms of this constant. Rather than prove this theorem, I used the difference of differences (the "second difference") to get at this second derivative, and then show that $|a/2| \leq 4$. Mar 19 answered Prove that $|a|+|b|+|c|\le17$ if $|ax^2+bx+c|\le1$ for $0\le x\le1$ Mar 19 answered Prove that there is a $c \in (a,b)$ such that $P(c)P'(c) = 0$ Mar 18 answered Suppose $f(z) \in H(D)$ is it possible to have… Mar 10 answered Prove that if $\lim_{x\to\infty} \frac{f(x)}{g(x)}=1$ then $\lim_{x\to\infty} \frac{\int_{x}^{\infty}f(t)dt}{\int_{x}^{\infty}g(t)dt}=1$ Mar 10 revised 100th derivative of $\frac{x^2+x}{2^x}$ at point 0 added 25 characters in body Mar 10 revised 100th derivative of $\frac{x^2+x}{2^x}$ at point 0 added 14 characters in body Mar 10 answered 100th derivative of $\frac{x^2+x}{2^x}$ at point 0 Mar 10 answered Convergence of $\sum \limits_{n=1}^{\infty}(-1)^{n+1}\frac{n}{n^2+1}$ Feb 13 awarded Enlightened Feb 13 awarded Nice Answer Feb 7 answered Prove $a_t \rightarrow x$ using the Betweenness Property Feb 7 comment $\lim_{n \to \infty}(\frac{a_n}{\sqrt{a_n^2+1}})=\frac{1}{2}$ - show that $a_n$ is convergent sequence gotta have fast fingers in this game... :) Feb 7 answered $\lim_{n \to \infty}(\frac{a_n}{\sqrt{a_n^2+1}})=\frac{1}{2}$ - show that $a_n$ is convergent sequence Jan 22 awarded Revival