Attaining the expected value over iterations
Is my implementation of the expected value correct? I conclude that the average number of iteration of this algorithm will be 1/3, but seems completely wrong. Rand() outputs either 0 or 1 (uniform)...
View ArticleShow $csc^2(pisigma)=frac{1}{pi^2}sum_{n=-infty}^{infty}frac{1}{(n+sigma)^2}$...
The full problem asked: Let $sigma$ be real, and not an integer. Find the complex form of the Fourier series for the $2pi$ periodic function $F(x)=e^{-isigma x}$ on $[-pi,pi]$. Use this and Parseval’s...
View ArticleWeighted sum of a convergent series
what can we say about $$lim_{nto infty}sum_{m=0}^nfrac{ma_m}{n+1-m}$$ if $sum |a_m|<infty$ I seem to be a bit off here. I have a stong feeling the the limit is zero. Can someone please provide some...
View ArticleHow to evaluate $sum_{k=1} ^{n-1} frac{sin (ktheta)}{sin theta}$
How to evaluate $$sum_{k=1} ^{n-1} frac{sin (ktheta)}{sin theta}$$ Any help ? I tried to use difference method. But I’m not getting there.
View ArticleProve expression is positive
Let $sum_i w_i=1$ and $w_i, x_i in mathbb{R}$, show that $$sum_i w_i x_i^4-sum_i w_i x_i sum_i w_i x_i^3geq 0. $$ I can show that $sum_i w_i x^2 -sum_i w_i x_i sum_i w_i x_i geq 0$ by convexity of the...
View Articlesimplifying summations
From knowing $7c=sum_{i=1}^{50-c}k_i$ and $cchoose 2 $=$ sum_{i=1}^{50-c}$ $k_ichoose 2 $ how can I get to $sum_{i=1}^{50-c}(k_i-mu)^2=(50-c)mu^2-14cmu+c^2+6c$ for some arbitrary $mu$? I would show you...
View ArticleSeparating variables from inequality. [duplicate]
This question already has an answer here: Factoring inequalities on Double Summation (Donald Knuth's Concrete Mathematics) 1 answer
View ArticleHow to compute the following series using taylor expansion manipulation?
How to compute $sum^{infty}_{n=0} frac{x^n}{(n+2)n!}$ and $sum^{infty}_{n=0}(-1)^n frac{(n+1)x^{2n+1}}{(2n+1)!}$ using taylor expansion manipulation? $1.sum^{infty}_{n=0}...
View ArticleSum of $1/n^k$ of the first $log P$ numbers
In a Udacity course I’m told the following: $sum_{i=1}^{log_2 (P)} 1/2^i = (P-1) /P $ I’ve checked that it’s true by entering it into Wolfram Alpha:...
View ArticleLimit of triple sum
Suppose one has the following triple sum: $$S_n=sum_{s=0}^nsum_{t=0}^ssum_{u=0}^sf(n,t)g(n,u)$$ where for all $n$, $-alpha< S_n <alpha$ for some real constant $alpha<infty$. Since $S_n$ is...
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