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0
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0answers
14 views

Convexity of a finite Sequence [migrated]

I was wondering how to determine whether the following set is convex or not: All $A_1, A_2,..., A_m $are convex sets: $ \sum^m_{i=1} A_i = \{ x_1+x_2+...+x_m,$ $ x_i \in A_i, i=1,2,...,m\}$ can I ...
1
vote
1answer
93 views

sequence of matrix multiplications

My linear algebra book has questions that are are marked to use math software. There's probably some $50 guide on how to do everything but usually documentation has gotten me through. I've been kind ...
0
votes
0answers
9 views

Cauchy sequences, not converging to zero [migrated]

True or False? If {x_n} and {y_n} are Cauchy and x_n + y_n > 0, for all natural n, then {1/(x_n + y_n)} cannot converge to zero. attempt:False: If both sequences are Cauchy, then they are convergent ...
3
votes
2answers
125 views

How to find a recurrence relation for a numerical sequence?

This question was inspired by Vladimir Reshetnikov's question (How to find a recurrence relation for a sequence?): Given a finite sequence of numbers, how can we find in MMA a recurrence relation ...
6
votes
1answer
86 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
1
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1answer
44 views

How to Solve a Sequence in Mathematica [duplicate]

Given the input and the output, how do you interpolate a function in Mathematica? For example if you know that $f(1)=\frac{1}{2}$, $f(2)=\frac{1}{3}$, $f(3)=\frac{1}{4}$,... how would you solve for ...
3
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0answers
48 views

Does it help to do any preprocessing before `FindSequenceFunction`?

I am always amazed how smart FindSequenceFunction can be in discovering general term formula for a sequence of rational numbers. The documentation says it can work ...
2
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2answers
198 views

Defining a sequence slot programmatically

This question is related to: Composition of functions using slots `Slot` (#) interfering with evaluation Consider a toy example: ...
0
votes
1answer
69 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
0
votes
1answer
92 views

Graphing the sequence {$p_k$} = $\frac{c - a + dp_{k-1}}{b}$ [duplicate]

Graphing the sequence {$p_k$} = $\frac{c - a + dp_{k-1}}{b}$ I need to know how to graph this function where it automatically plugs in the previous term for $p_{k-1}$, the coefficients are of my ...
0
votes
1answer
75 views

Creating If statements programmatically [duplicate]

I want to write an algorithm that returns a sequence of numbers, starting from a specified point but stopping once a criterion has been reached. For example ...
2
votes
0answers
130 views

Faster Ways to compute recursive summation

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
2
votes
1answer
54 views

Matching a list of sequences with common form

I am trying to find a pattern that matches a list of sequences that share a common form. The sequence form is: 1 followed by zero or more nonzero integers, followed by 0. An example list is: ...
1
vote
0answers
106 views

Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
3
votes
0answers
58 views

How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
2
votes
2answers
100 views

Problem on Consecutive Sequence Sums that are Squares

Here is a seemingly simple Problem: I have two natural numbers n and m, n < m such that S1:= n +...+ m is a square and also S2:= n +...+ m + (m+1) is a square. Problem a) : Find n and m. You ...
2
votes
0answers
73 views

Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity]

I would like to show that the following (and other similar formulae) tends to zero. Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity] What's the right ...
1
vote
1answer
131 views

Defining a recursive integral sequence

I have a recursive integral sequence as follows: $$y_0(x)=1+r,$$ $$y_1(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_0(t) dt,$$ $$\vdots$$ $$y_n(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_{n-1}(t) ...
5
votes
5answers
1k views

How to detect if a sequence of integers is consecutive

I'm not a math-guy really (a programmer actually) and this is my first question. And excuse me if I can not explain my problem good. The problem is I have a sequence of integers and I want to detect ...
0
votes
2answers
84 views

Sum of first n items in a sequence [closed]

What's a way to sum over the first n items in a sequence, for example the sequence defined by $2^{k-1}\cdot k$ for $k\in\mathbb{Z},k>0$? I do these by hand all the time but am a bit tired of doing ...
2
votes
2answers
169 views

Generation function of recurrence sequence

I'm trying to find generation function of recurrence sequence ...
4
votes
3answers
158 views

Long waiting time for computing a summation

It takes a long time to compute the summation below, and I'd like to know if there are alternative ways to compute things faster. When replacing $15$ by $\infty$, then I should get $3^{1/3}$. I need ...
2
votes
1answer
204 views

how can I solve integrals including recursion of some sequences of functions

I would like to solve the equations as given below in mathematica. I have written some codes before but I have no idea when there is sub indexing to indicate the series of functions. I will be very ...
2
votes
1answer
127 views

Match a sequence of integers

I would to match a pattern p1 = 0,0,1,0,0 to the elements in listA. The elements are a boolean sequence that may look like this ...
1
vote
1answer
98 views

How to define Similarity Rules?

I have a question about Mathematica's SimilarityRules defining (for e.g. SequenceAlignment function). So help centre clearly ...
9
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1answer
332 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
2
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1answer
127 views

Generating a list of specific intermediate numbers associated with continued fractions

First of all, I don't know how ContinuedFraction[] or Convergents[] are implemeneted, and I think it is immaterial to my ...
-3
votes
1answer
155 views

Limit of a subsequence

I am trying to calculate limit for a subsequence <${ a }_{ {n }^{ 2} }$> because I was trying to see that limits of sequences and subsequences are both same. I was able to generate the sum for ...
5
votes
1answer
138 views

Find the domain in which a sequence converges

I seem to have a lot of problems in the format of: Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges. However, ...
11
votes
4answers
620 views

How can I return a Sequence?

Recently I had the need to redefine a certain symbol in my init.m so it would be automatically omitted from any lists it appears in. I decided to redefine it to an empty sequence, e.g. ...