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Mar
4
answered Find $\lim_\limits{x\to 0}\left({\tan x\over x}\right)^{1\over 1-\cos x}$.
Mar
4
comment Number of distinct terms in the expansion of $\big(x+\frac{1}{x}+x^2+\frac{1}{x^2}\big)^{15}$
I believe it is $(x^4+x^3+x+1)^{15}$
Mar
4
answered Number of distinct terms in the expansion of $\big(x+\frac{1}{x}+x^2+\frac{1}{x^2}\big)^{15}$
Mar
4
comment Binomial Theorem and Summation
This is known as Vandermonde's Identity
Mar
4
revised How can I solve this recurrence relation?
expand the explanation
Mar
4
answered How can I solve this recurrence relation?
Mar
4
answered The fly and its owner
Mar
3
answered How to solve nonhomgenous recurrence relation?
Mar
3
comment If $n$ is an odd integer prove that $n - 2^k$ is divisible by $3$
Unless one redefines "odd" to mean "not divisible by $3$" instead of "not divisible by $2$", but that is absurd, too.
Mar
3
revised How to define a subset with proper mathematical notation
edited tags
Mar
3
comment How to define a subset with proper mathematical notation
This should really be asked on the main site, not meta.
Mar
3
answered Probability Question about Eyes
Mar
3
revised Integrating $\sec\theta\tan^2\theta d\,\theta$
do the partial fractions
Mar
3
answered Integrating $\sec\theta\tan^2\theta d\,\theta$
Mar
3
comment Prove that there is no perfect square that is congruent to 2 mod 10 and 3 mod 10.
To be more precise, you are saying that the quadratic residues mod $10$ are $\{0,1,4,5,6,9\}$.
Mar
3
answered Finding the largest constant $C$ such that $|\ln x−\ln y| \geq C|x−y|$ for all $x, y \in (0, 1]$
Mar
3
comment Doubt in the defn of exponential operator.
Yes. Just plain scalar multiplication.
Mar
3
answered Doubt in the defn of exponential operator.
Mar
3
comment If $\int_{\mathbb{R}}\vert f\vert<\infty$, then $\sum_{n=1}^\infty\vert n\int_n^{n+1/n}f(x+y)dy\vert<\infty$
@cap: any interval $[y-k-1,y-k]$ of length $1$ must be contained in an an interval $[m,m+2]$ where $m\in\mathbb{Z}$. Note that $$\int_m^{m+2}\psi(x)\,\mathrm{d}x=\left\{\begin{array}{}2&\text{if }m\ge1\\1&\text{if }m=0\\0&\text{if }m\lt0\end{array}\right.$$ therefore, $$\int_{y-k-1}^{y-k}\psi(x)\,\mathrm{d}x\le2$$
Mar
3
answered Show that if $f : \mathbb{R}^{2} \to \mathbb{R}$ continuously differetiable then $f$ is not inyective