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NightRa
  • Member for 10 years, 9 months
  • Last seen more than 2 years ago
18 votes
3 answers
21k views

Choosing numbers without consecutive numbers.

10 votes
2 answers
135 views

Sum of radicals greater than 1

10 votes
6 answers
15k views

Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $

8 votes
3 answers
4k views

Number of binary strings with $n$ ones and $m$ zeros

6 votes
1 answer
935 views

Convergence of sum of sequences and product of sequences implies convergence sum of sqares of sequences.

6 votes
9 answers
592 views

Limit of $\lim_{x\to\infty}{\frac{\cos(\frac{1}{x})-1}{\cos(\frac{2}{x})-1}}$

4 votes
3 answers
8k views

Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$

3 votes
3 answers
974 views

Prove that $\lim \limits _{n \to \infty} \left( n - \frac 1 {e^{\frac 1 n} - 1} \right) = \frac 1 2$

3 votes
1 answer
139 views

Probability of random subsets of the same size intersecting

3 votes
1 answer
159 views

Limit of $a_n=f(1)+f\left(\frac{1}{2}\right)+f\left(\frac{1}{3}\right)+...+f\left(\frac{1}{n}\right)$

3 votes
1 answer
34 views

Transitiveness of set sizes

3 votes
2 answers
192 views

Taylor expansion

2 votes
5 answers
822 views

Prove convergence and find limit of $a_{n+2}=\frac{1}{2}(a_n+a_{n+1})$

2 votes
3 answers
110 views

Probability of Binomial twice of Geometric

2 votes
2 answers
437 views

Combinatorical proof $\sum\limits_{k=0}^n{{2n+1}\choose k}=2^{2n}$

1 vote
2 answers
272 views

Prove combinatoric inequality: ${n \choose {j+k}}\le {n \choose j}{{n-j}\choose k}$

1 vote
1 answer
240 views

Recursive and closed form solution for choosing $n$ pairs/triplets.. of $kn$ elements.

1 vote
1 answer
28 views

Parametrized complex equation

1 vote
1 answer
26 views

If a symmetric bi-liear form is positive, then $a_{11}\cdot a_{nn}>a_{n1}\cdot a_{1n}$

1 vote
3 answers
2k views

Symmetric matrix congruency

1 vote
1 answer
120 views

Combinatorial proof of $1=\sum_{i=0}^n{(-1)^i \binom{n}{i} 2^{n-i}}$

1 vote
4 answers
100 views

Limit of $\lim_{x \to \infty}{x^{\frac{5}{3}}\cdot[{(x+\sin{\frac{1}{x}})}^{\frac{1}{3}} -x^{\frac{1}{3}}]}$

1 vote
2 answers
103 views

Seating robots in a row

1 vote
3 answers
2k views

If a is less than 1 in absolute value, than n times a to the n'th power converges to zero [duplicate]

1 vote
4 answers
89 views

Exponential algebra problem

1 vote
1 answer
155 views

Evaluating $\lim_{x\to0}{x^x}$ [duplicate]

1 vote
2 answers
341 views

Counting votes, as long as one has more votes all the way through.

0 votes
1 answer
2k views

Proving a subset of the natural numbers has a minimal element [duplicate]

0 votes
2 answers
46 views

Relation between sequences is the same as the relation between their limits