Questions tagged [sequence]
Questions on specifying order in and splicing of lists, including use of Mathematica Sequence objects.
206 questions
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How to code a recursive algorithm to exponentiate $e^{1/e}$ to itself indefinitely and hence show that this sequence converges to $e$?
I seek help coding an algorithm that shows when $e^{1/e}$ is repeatedly raised to itself it will eventually converge to $e$. The context for this post comes from this same question on M.SE:
What ...
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How do I set up a recursive algorithm to repeatedly square root a positive real number?
From real analysis, I was asked the following question:
What happens when you hit the square root key repeatedly on a calculator for any initial positive number $x$? Formulate this question in terms ...
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Numerical handling within Manipulate[] with variable number of parameters
This is a minimal example of a more complex problem. I need to build the Manipulate function as below with a variable number of parameters, which is why ...
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Finding the Sequence of Eigenvalues for an 𝑛 × 𝑛 Matrix with Structured Elements in Mathematica
Suppose we have an $n*n$ matrix whose elements follow a known sequence. Additionally, the eigenvalues of these matrices also form a sequence. for example sppose the below matrix
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Arithmetic and Geometric Sequences Problem
Let $an$ be an arithmetic sequence with common difference d, and $bn$ be a geometric sequence with common ratio q. It is known that the sum of the first n terms of the sequence ${an + bn}$ is $sn = n^...
user105429
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The summation formula of a sequence after adding the absolute value to its general term
a[n_] = 2^n - 4
s[n_] = Sum[Abs@a[k], {k, 1, n}]
The summation formula obtained after adding the absolute value to the general term is this:
...
user105429
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How to Speed Up the Summation of a Sequence?
A sequence (a_n) is given with a recursive formula, and another new sequence (b_n) is formed by the remainders of each term of (a_n) divided by 3. When calculating the sum of the first 2022 terms of ...
user104677
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We would like to define $k$ in advance as an even number
Can we define in advance that $k$ is even?
For example, when defining the sequence $\{a_n\}$ inductively as follows,
input:
...
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Max Geometric Sequences
We start with a number, say 12. Then try to find how many different 3-number geometric sequences exist below (up to and including) that number.
Ex: below 12, there are 4 such sets:
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How to display cumulative values separately with an ellipsis in the middle?
a[n_] = a (1 + t)^-n
t[n_] = Sum[a[k], {k, 1, n}]
The result obtained above is as follows:
(a (1 + t)^-n (-1 + (1 + t)^n))/t
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user103289
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Defining a sequence from a list or a table
I want to define a sequence from a list.
For example if I have the list
A={1, 2, 3, 34, -9, 18}
I want to define the sequence ...
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How to find a closed form for this pattern (if it exists)?
Suppose we have the following code:
...
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How to solve this problem combining sequences and reasoning using code?
QUESTION:
Let $m$ be a positive integer, and let $a_1, a_2, ..., a_{4m+2}$ be an arithmetic sequence with non-zero common difference. If removing two terms $a_i$ and $a_j$ ($i < j$) leaves $4m$ ...
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Convergence of $\left\{n!\sum_{k=1}^{n!}\frac{1}{k^{\frac{3}{2}}}\right\}$ as $n\to \infty$ using Mathematica or otherwise
Using Mathematica or otherwise, I need to find the convergence or divergence
of$$\lim_{n\to\infty}\left\{n!\sum_{k=1}^{n!}\frac{1}{k^{\frac{3}{2}}}\right\}$$ where $\{x\}$ denotes the fractional part ...
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How to display the specific general term formula of Fibonacci sequence? [closed]
RSolve[{a[n] == a[n - 1] + a[n - 2], a[1] == 1, a[2] == 1}, a[n],
n]
The general term formula obtained by the above code is:
...
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