Question of the Day
Posted on08 Dec 2020
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If $a_n$ is a bounded monotonically increasing sequence prove then that $b_n = \frac{a_1 + \cdots + a_n}{n}$ is also bounded and... Read More
Question of the Day
Posted on07 Dec 2020
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Prove that a bounded monotone increasing sequence is convergent.
Question of the Day
Posted on06 Dec 2020
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Find the Taylor Series expansion of $\cosh x$ at the point $a=0$ and show that the remainder convergences to zero over $\left(-r,r\right)$... Read More
Question of the Day
Posted on05 Dec 2020
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For what values of rational $p$ and $q$ will $p\sqrt{2}+q\sqrt[3]{3}$ be rational? You may assume $\sqrt[3]{3}$ is irrational and of course $\sqrt{2}$... Read More
Question of the Day
Posted on04 Dec 2020
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Calculate $ \lim\limits_{n \to \infty } \sum \limits_{k=1}^n 4^{-k} $.
Question of the Day
Posted on03 Dec 2020
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Calculate the limit $ \lim\limits_{n \to \infty } \frac{\left(n^2+3\right)^\frac{1}{2}}{\left(n^2+2\right)^\frac{1}{3}} $.
Question of the Day
Posted on02 Dec 2020
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Calculate the limit $ \lim\limits_{n \to \infty } \cos \frac{1}{\sqrt{n}}} $.
Question of the Day
Posted on01 Dec 2020
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For what values of $x$ will the following converge absolutely? $\sum\limits_{n=1}^\infty \frac{\left(3x-2\right)^n}{n}$
Question of the Day
Posted on30 Nov 2020
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For what values of $x$ will the following converge absolutely? $\sum\limits_{n=1}^\infty n! x^n$
Question of the Day
Posted on29 Nov 2020
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For what values of $x$ will the following converge absolutely? $\sum\limits_{n=1}^\infty 3^n \frac{ x^n }{ n! } $