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asd
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7 votes
2 answers
2k views

In how many ways is possible to write a number as the ordered sum of $1$ and $2$

6 votes
2 answers
109 views

If $f$ is differentiable on $[1,2]$, then $\exists \alpha\in(1,2): f(2)-f(1) = \frac{\alpha^2}{2}f'(\alpha)$

6 votes
2 answers
5k views

Proof by induction: $(1+x)^n > 1 + nx+nx^2$

6 votes
2 answers
509 views

Help to understand this property: $\int\limits_{ka}^{kb}s\left(\frac{x}{k}\right)dx = k\int\limits_a^bs(x)dx$

6 votes
3 answers
2k views

Let $G$ be a group. Show that $\forall a, b, c \in G$, the elements $abc, bca, cab$ have the same order.

5 votes
5 answers
364 views

Calculate: $177^{20^{100500}}\pmod{60}$

5 votes
1 answer
966 views

Representing a nonnegative integer as the ordered sum of odd numbers

5 votes
5 answers
9k views

What's wrong?: Find the infinite sum $S = 1 + \frac{3}{4} + \frac{7}{16} + \frac{15}{64} + \frac{31}{256} + \ldots$

5 votes
1 answer
4k views

Prove: In a ⊿, the bisector of the right angle bisects the Altitude and Median drawn from that same vertex.

5 votes
3 answers
188 views

Proof: $n^p < \frac{(n+1)^{p+1}-n^{p+1}}{p+1} < (n+1)^p$

4 votes
2 answers
6k views

Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$

4 votes
2 answers
306 views

Proof: $2\sqrt{m}-2 < \sum\limits_{n=1}^m\frac{1}{\sqrt{n}}< 2\sqrt{m}-1$

4 votes
4 answers
988 views

What is the relationship between the Archimedean Property and Calculus?

4 votes
2 answers
1k views

How to derive this formula: $\int_a^bf(c-x)dx = \int_{c-b}^{c-a}f(x)dx$?

4 votes
1 answer
431 views

Sum of binomial coefficients from $\binom{2m+1}{0}$ to $ \binom{2m+1}{m} $

4 votes
1 answer
102 views

For every $n$, $\sum\limits_{m=0}^{\infty}\left(-\frac{1}{2}\right)^m\sum\limits_{l=0}^m\left(\frac{1}{2^{n-1}}-2\right)^{m-l} {n \choose l}=1$

3 votes
1 answer
69 views

Taylor series of $\frac{x-2}{\sqrt{x^2-4x+8}}$ at $x = 2$. Where is the mistake?

3 votes
2 answers
81 views

Is the set $C = \{( x_1, x_2, x_3, x_4) \in \mathbb{R}^4: x_1^2 + x_2^2 + x_3^2 < \ln(1+x_4^2)\}$ open or closed or neither?

3 votes
2 answers
242 views

Show that in $\lim_{x\to 0}\frac{x^3\sin(1/x)}{\sin^2 x}$ can't be applied L'Hopital's Rule

3 votes
5 answers
2k views

Find the $n$ derivative of $y= e^{2x}\sin^2 x$

3 votes
3 answers
489 views

Can the inequality $\sum\limits_{i=1}^n\frac{1}{\sqrt{i}} < 2\sqrt{n} - 1$ be proved without induction?

3 votes
1 answer
135 views

What is the significance of proving the integrability of monotonic functions?

3 votes
1 answer
3k views

Finding the number of primes numbers using exclusion/inclusion principle: What am I doing wrong?

2 votes
1 answer
154 views

Investigating the differentiability of $f(x) = |\sin x |$

2 votes
2 answers
116 views

Investigating the differentiability of $f(x) = |\pi x|sinx$

2 votes
0 answers
83 views

Alternating sum of subfactorials: Is there a closed form for this: $\displaystyle \sum_{i=0}^{m-2}(-1)^i\left[\frac{(m-i)!}{e}\right]$?

2 votes
2 answers
125 views

$\nabla \times \left(\frac{\mathbf{A \times r}}{r^3}\right)$, where $\mathbf{A}$ is independent of $\displaystyle\nabla \times$

2 votes
1 answer
610 views

Confusion in understanding a proof in Apostol's Calculus I

2 votes
0 answers
174 views

Is it correct to say that if $\lim\limits_{x \to a}f(x) = 0$ it is an Infinitesimal?

2 votes
3 answers
1k views

Prove that: $\lim\limits_{x \to +\infty}\frac{(\log x)^b}{x^a} = 0$ and $\lim\limits_{x \to +\infty}\frac{x^b}{e^{ax}} = 0$