All Questions
2
questions
0
votes
1
answer
96
views
Find a recursive formula for a closed formula recursively at infinity
I have a recursive sequence defined as such:
$$
\left(u_k \right) = \begin{cases}
u_0 = 1 \\
u_k = u_{k-1} + u_{k-1} \cdot \frac{1}{n}
\end{cases}\quad \text{with}\...
- 936
2
votes
2
answers
167
views
$ a_n = \frac{a_{n-1}(a_{n-1} + 1)}{a_{n-2}}.$ and $ T = 3.73205080..$?
Consider the following sequence :
Let $a_1 = a_2 = 1.$
For integer $ n > 2 : $
$$a_n = \frac{a_{n-1}(a_{n-1} + 1)}{a_{n-2}}.$$
$$ T = \lim_{k \to \infty} \frac{a_k}{ a_{k - 1}}.$$
$$T = ??$$
...
- 16.4k