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! } $
Question of the Day
Posted on28 Nov 2020
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For what values of $x$ will the following converge absolutely? $\sum\limits_{n=1}^\infty \left(-1\right)^{n-1} \frac{ x^n }{ n } $
Question of the Day
Posted on27 Nov 2020
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Given that $0 < a < b$ prove $a < \sqrt{ab} < b$ and $ \sqrt{ab} < \frac{a+b}{2}$
Question of the Day
Posted on26 Nov 2020
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Prove by induction that $1^3 + 2^3 + \cdots + k^3 = \left(1+2+\cdots+k\right)^2$.
Question of the Day
Posted on25 Nov 2020
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Given that $\sum\limits_{n=1}^\infty b_n $ is a convergent series of positive terms prove that series $\sum\limits_{n=1}^\infty a_n $ of positive terms will... Read More