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- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Signals_and_Systems_(Baraniuk_et_al.)/16%3A_Appendix_C-_Analysis_Topics_Overview/16.02%3A_Convergence_of_SequencesThis module will present an introduction into convergence and focus on what a sequence is and how it behaves as it approaches infinity.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_Languages/Python_Programming_(OpenStax)/03%3A_Objects/3.05%3A_Tuple_BasicsThis page discusses tuples in programming, detailing their features like immutability, which enhances memory efficiency and performance. It covers the structure of tuples, accessed via indexing, and c...This page discusses tuples in programming, detailing their features like immutability, which enhances memory efficiency and performance. It covers the structure of tuples, accessed via indexing, and contrasts them with mutable lists. The section also includes practical examples, creation and manipulation techniques, and the use of the `tuple()` function to create tuples from lists.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_Languages/Python_Programming_(OpenStax)/05%3A_Loops/5.01%3A_While_LoopThis page explains Python's while loop, detailing its functionality to repeatedly execute code while a condition is true. It offers examples like generating Fibonacci numbers and counting odd numbers,...This page explains Python's while loop, detailing its functionality to repeatedly execute code while a condition is true. It offers examples like generating Fibonacci numbers and counting odd numbers, alongside checkpoints and exercises to enhance comprehension. Users are encouraged to apply while loops in practical tasks, such as handling user inputs and calculating sums of odd integers within specified ranges.
- https://eng.libretexts.org/Bookshelves/Introductory_Engineering/EGR_1010%3A_Introduction_to_Engineering_for_Engineers_and_Scientists/14%3A_Fundamentals_of_Engineering/14.02%3A_Arithmetic/14.2.06%3A_Sequences_and_Series/14.2.6.02%3A_SequencesIn this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits f...In this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits for functions discussed earlier. We close this section with the Monotone Convergence Theorem, a tool we can use to prove that certain types of sequences converge.
- https://eng.libretexts.org/Courses/Oxnard_College/Matlab_and_Octave_Programming_for_STEM_Applications_(Smith)/02%3A_MATLAB_Octave_Scripts/2.05%3A_The_Fibonacci_SequenceThe Fibonacci sequence, denoted \(F\), is a sequence of numbers where each number is the sum of the previous two. The following expression computes the \(n\)th Fibonacci number: \[F_n = \frac{1}{\sqrt...The Fibonacci sequence, denoted \(F\), is a sequence of numbers where each number is the sum of the previous two. The following expression computes the \(n\)th Fibonacci number: \[F_n = \frac{1}{\sqrt{5}} \left[ \left( \frac{1 + \sqrt{5}}{2} \right)^{n} - \left( \frac{1 - \sqrt{5}}{2} \right)^{n} \right] \notag\] In this example, the message says the error is in fibonacci, but the actual problem is that we have not assigned a value to n.
- https://eng.libretexts.org/Courses/Oxnard_College/Matlab_and_Octave_Programming_for_STEM_Applications_(Smith)/04%3A_Vectors/4.06%3A_Vectors_and_SequencesFor example, another way to evaluate the Fibonacci sequence from Chapter 2 is to store successive values in a vector. Remember that the definition of the Fibonacci sequence is \(F_1 = 1\), \(F_2 = 1\)...For example, another way to evaluate the Fibonacci sequence from Chapter 2 is to store successive values in a vector. Remember that the definition of the Fibonacci sequence is \(F_1 = 1\), \(F_2 = 1\), and \(F_{i} = F_{i-1} + F_{i-2}\) for \(i > 2\). Listing 4.1 shows how we can compute the elements of this sequence and store them in a vector, using a capital letter for the vector F and lower-case letters for the integers i and n.
- https://eng.libretexts.org/Courses/Oxnard_College/Matlab_and_Octave_Programming_for_STEM_Applications_(Smith)/03%3A_for_Loops_Ploting_Points_Sequences_and_Series/3.11%3A_Chapter_ReviewA loop variable is a variable that gets assigned a different value each time through the loop. An accumulator is a variable that is used to accumulate a result a little bit at a time. The numbers that...A loop variable is a variable that gets assigned a different value each time through the loop. An accumulator is a variable that is used to accumulate a result a little bit at a time. The numbers that make up the sequence are called . A series is the sum of a sequence of elements. Generalization is a way to make a program more versatile, for example, by replacing a specific value with a variable that can have any value.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Databases_and_Data_Structures/Open_Data_Structures_-_An_Introduction_(Morin)/08%3A_Scapegoat_Trees/8.02%3A_Discussion_and_ExercisesReimplement the \(\mathtt{rebuild(u)}\) method discussed at the beginning of this chapter so that it does not require the use of an array to store the nodes of the subtree being rebuilt. The \(\mathtt...Reimplement the \(\mathtt{rebuild(u)}\) method discussed at the beginning of this chapter so that it does not require the use of an array to store the nodes of the subtree being rebuilt. The \(\mathtt{add(x)}\) and \(\mathtt{remove(x)}\) operations are identical to the standard BinarySearchTree operations, except that any time the balance invariant is violated at a node \(\mathtt{u}\), the subtree rooted at \(\texttt{u.parent}\) is rebuilt.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_Languages/Python_Programming_(OpenStax)/05%3A_Loops/5.02%3A_For_LoopThis page explains the for loop construct in Python, highlighting its use for iterating over containers like ranges, strings, and lists. It covers the range() function for sequence generation and incl...This page explains the for loop construct in Python, highlighting its use for iterating over containers like ranges, strings, and lists. It covers the range() function for sequence generation and includes practical examples and exercises. Users can practice tasks like counting characters and printing number sequences while assessing their understanding through checkpoints. Specific programming exercises, such as counting spaces in a string and identifying even and odd numbers, reinforce skills.
