All Questions
5
questions with no upvoted or accepted answers
2
votes
0
answers
150
views
Evaluate this product $n \times \frac{n-1}{2} \times \dots \times \frac{n-(2^k-1)}{2^k}$
For $k = \lfloor \log_{2}(n+1) \rfloor - 1$ evaluate
$n \times \frac{n-1}{2} \times\frac{n-3}{4} \times \frac{n-7}{8} \times \dots \times \frac{n-(2^{k}-1)}{2^k}$
So the product goes up to $k$ and I ...
- 69
1
vote
1
answer
45
views
Sum and product problem
How can I find the result of:
$\sum\limits_{i=1}^{n}\prod\limits_{j=1}^{2} ij$
I know that $\prod\limits_{j=1}^{2} ij = 2i^2$, so I should simply do the summation as $\sum\limits_{i=1}^n2i^2$?
1
vote
0
answers
48
views
Transforming a long sum of products for efficient computation (based on spanning trees in a complete graph)
Let's say there is a set of $n$ real coefficients: $a_1,...,a_n$. My task is to calculate the value of a rather simple sum of k products: ...
- 239
1
vote
0
answers
35
views
Help with simplification of this expression.
So i have derived this expression and would like to simplify it (i.e find an expression purely in terms of J and v).
$$ J\bigg[1+\sum_{n=1}^{J-1}\prod_{k=1}^{n}\frac{k(1-v)(J-k)}{(k+1)(J-k-1 + vk)}\...
- 61
0
votes
0
answers
45
views
Inequality with Products and Sums
I need help to find a proof for the following inquality.
Assuming that $ 0 \leq c_i \leq 1 $ and $ 0 \leq d_i \leq 1 $, show that
$$
\prod_{i=1}^N (c_i + d_i - c_i d_i) \geq \prod_{i=1}^N c_i + \prod_{...
- 778