### 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

### Question of the Day

Posted on24 Nov 2020

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Show that $\sum\limits_{n=1}^\infty \frac{\sin n}{ n } $ converges.

### Question of the Day

Posted on23 Nov 2020

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Prove that the remainder $R_k$ in the Taylor series expansion of $\cos x$ at the point $a=0$ will converge for all values...Read More

### Question of the Day

Posted on22 Nov 2020

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Find the limit of $ \lim\limits_{n \to \infty } \frac{r^n}{n!} $, where $r$ is a positive real non-zero number.

### Question of the Day

Posted on21 Nov 2020

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Prove that $-\pi+\sqrt{5+\pi^2}$ is irrational.