# hkju

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# 18 Questions

 15 Find the number of arrangements of $k \mbox{ }1'$s, $k \mbox{ }2'$s, $\cdots, k \mbox{ }n'$s - total $kn$ cards. 6 Provide different proofs for the following equality. 4 Evaluation of $\int_{-v/2}^{v/2} \sqrt{1-\left(\frac{t}{7}-\frac{v}{14}\right)^2} \sqrt{1-\left(\frac{t}{7}+\frac{v}{14}\right)^2} dt$ 4 Find the expected value of a dice sum 2 Equivalent condition for the divisibility by $2^{n-1}$.

# 442 Reputation

 +20 Evaluation of $\int_{-v/2}^{v/2} \sqrt{1-\left(\frac{t}{7}-\frac{v}{14}\right)^2} \sqrt{1-\left(\frac{t}{7}+\frac{v}{14}\right)^2} dt$ +10 Equivalent condition for the divisibility by $2^{n-1}$. +10 what is the value of the following sum? +5 Can we express the following ordinary generating function?

# 12 Answers

 3 Question about sum 2 Find the power series expansion of $f(z)=z^2$ around $z = 2$ 1 Can we express the following ordinary generating function? 1 why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$ 1 Prove that $n! = \sum_{i=0}^{n-1}{n \choose i}(n-i)^n (-1)^i$

# 30 Tags

 3 combinatorics × 8 1 binomial-coefficients × 2 3 sequences-and-series × 4 1 limits × 2 2 polynomials × 3 1 summation × 2 2 complex-analysis × 2 0 pde × 2 1 calculus × 3 0 generating-functions × 2

# 3 Accounts

 Mathematics 442 rep 311 MathOverflow 112 rep 5 Programmers 101 rep

# 13 Badges

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