# Tagged Questions

Questions regarding functions defined recursively, such as the Fibonacci sequence.

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### Solving recurrence relation using Master Method

How to solve following recurrence relation?? $T(2n) = T(2n-20) + n.$ And if there is any other way despite Master's method to do this simpler way, what is it?
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### Limit of a recurrence

I was given the following exercise as homework: find the limit of $b_{n+1} = \sqrt{2 + b_n}$, $b_1 = \sqrt{2}$, with a hint that $b_n < 2 \forall n \in \mathbb{N}$. I have proven that $b_n$ is ...
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### Understanding two “triangular” sequences

Just playing around doodling today and I happened across two related sequences of numbers and I'm reaching out to understand what exactly is going on. Sequence 1 The $n$th term of Sequence 1, $a_n$, ...
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### Is there any way to compute these sums quickly?

I have a sum of the following form (all numbers are positive integers): $$F(p) = \sum_{x=1}^{N} a_x x^p$$ Where $N$ and all $a_x$ terms are known/fixed constants. However I need to be able to ...
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### How to solve this nonlinear difference equation $a_{n+1} = 2a_n + \frac{1}{a_n}$, $a_1 = 1$? [duplicate]

How to solve this nonlinear difference equation $$a_{n+1} = 2a_n + \frac{1}{a_n},\quad a_1 = 1.$$