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Results tagged with limits-and-convergence
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user 45564
Convergence of series, sequences and functions and different modes of convergence.
8
votes
1
answer
675
views
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left...
What is $$\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{-k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$$
- 3,377
27
votes
5
answers
3k
views
How to show a function converges to 1
Consider the following recurrence relation in two variables:
$$f(a, b) = \frac{a}{a+b} f(a-1,b)+ \frac{b}{a+b}f(a+1,b-1) $$
for positive integers $a$ and $b$,
with the boundary conditions $f(0,b)=0$ f …
- 3,377