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GoodDeeds
  • Member for 8 years, 1 month
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43 votes

If there are $74$ heads and $196$ legs, how many horses and humans are there?

17 votes

Proof that square of an $\sqrt{2 - 4q}$ is not an integer

16 votes
Accepted

Prove that $n$ is also a power of $2$.

16 votes
Accepted

Is there a perfect square in the sequence $6, 96, 996, 9996, ... , 99999...996, ...$?

16 votes
Accepted

Subtracting empty set from another

14 votes

Subsets of sets containing empty set

12 votes

How many solutions for an equation with simple restrictions

12 votes
Accepted

Assume $f :[0,1] \rightarrow [0,1]$ is a continuous function. Show there exists a fixed point $x$, i.e. $f(x) = x$

11 votes
Accepted

$\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to :

11 votes

If $f(x)$ is discontinuous at 0, does that mean $f(x) + \frac{1}{f(x)}$ is also discontinuous?

10 votes

Find the value of $(a - b)^2$ given $a + b = 2$ and $a^2 + b^2 = 6$

10 votes

How many binary digits does $2^{100}$ have if written in base $2$?

9 votes
Accepted

Integrating $\int^2_{-2}\frac{x^2}{1+5^x}$

9 votes

Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?

8 votes
Accepted

Combinatorics: Why isn't $(^{20}C_{12}) ≠ (^{20}C_{11})(^9C_1)$?

8 votes
Accepted

Evaluation of $\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$

8 votes
Accepted

Power set of a set with an empty set

7 votes
Accepted

prove that the supremum is $\sqrt{2}$

7 votes

How do you solve the following separable differential equation: y'y = y + 1?

6 votes
Accepted

How does the concept of a derivative solve the problem of instantaneous velocity?

6 votes
Accepted

Function expressed the sum of an odd and even function

6 votes

Explain why any composite three-digit number is divisible by at least one of the primes 2,3,5,7,11,13,17,19,23,29,31.

6 votes
Accepted

Convergent or divergent: $\sum_{k=1}^{\infty}\frac{2^{k}\cdot k!}{k^{k}}$

6 votes
Accepted

Find a closed-form expression for $\binom n1+3\binom n3+5\binom n5+\cdots ,$ where $n > 1$.

6 votes
Accepted

Simplifying radicals inside radicals: $\sqrt{24+8\sqrt{5}}$

6 votes
Accepted

Evaluate $\int \frac{\sqrt{x}+1}{\left(\sqrt[3]{x}-1\right)\sqrt[6]{x^5}}\,dx$

6 votes
Accepted

Number of common roots of $x^3 + 2 x^2 +2x +1 = 0$ and $x^{200} + x^{130} + 1 = 0 $

6 votes
Accepted

Prove with use of derivative

6 votes
Accepted

Finding the $n$-th derivative of $f(x)=e^{x}\sin(x)$

6 votes
Accepted

The sum of three consecutive terms of an Arithmetic progression is $18$ and their product is $120$. Find the terms.

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