Tagged Questions
0
votes
1answer
87 views
A hard limit with integral sign
$$\displaystyle\underset{m\to +\infty }{\mathop{\lim }}\,\left[ \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\int_{0}^{x}{{{\left( \underset{n\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{1}{n} ...
6
votes
4answers
152 views
Help evaluating a limit
I have the following limit:
$$\lim_{n\rightarrow\infty}e^{-\alpha\sqrt{n}}\sum_{k=0}^{n-1}2^{-n-k} {{n-1+k}\choose k}\sum_{m=0}^{n-1-k}\frac{(\alpha\sqrt{n})^m}{m!}$$
where $\alpha>0$.
...
1
vote
1answer
49 views
The limit of a sum with elements from 2 sequences
Let's consider the sequence of real numbers $(a_{n}),n\geq1,a_{1}>0$ that satisfies the following recurrence:
$$\frac{n(n+2)}{(n+1)}a_{n}-\frac{n^2-1}{n}a_{n+1}=n(n+1)a_{n}a_{n+1}$$
I'm supposed ...
