# Tagged Questions

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### What does ! mean in sequences?

I'm doing a sequences problem where I have to write the first five terms of a sequence. It looks normal, but there is an exclamation mark on the denominator: $$a_n = \frac{1}{(n + 1)!}$$ & ...
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### Represent loop nests as multiple summations?

This may be trivial but I would appreciate if someone could point me in the right direction here.. I am trying to express the number of instances in a loop nest in a general form. As a mathematical ...
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### Convert for-loop into mathematical expression

I'm facing a simple problem actually: for (int i = 0; i < noutput_items; i++){ out[i] = in[i] * in[i]; } When I want to formalize this as a math ...
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### Sequence Notation

I have come across the following in the book "Principles of Program Analysis" by Nielson, Nielson and Hankin to represent a sequence and I am unsure of what its constituent parts mean. Obviously ...
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### Big O notation, $1/(1-x)$ series

I am doing calculus and I find this notation extremely confusing even after reading textbook and notes. Here is a question I was trying to do and I think I cannot do this yet because I dont fully ...
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### What is the summation operator used for in Mathematics?

I am quite experienced in programming and I know that summation in math is similar to a for loop: It runs the specified operations for $x$ amount of times. What I want to know is how this is useful in ...
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### Eventually always notation

Let $X$ be a set and $A\subset X$. For a sequence $F = (f_n)_{n\geq 0}$ of elements of $X$ we say that $F$ is eventually always in $A$ if for some $N\geq0$ it holds that $f_n\in A$ for all $n\geq N$. ...
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### Notation for a subsequence of a sequence

If we have a sequence (an ordered list) $$S=(s_0,s_1,...,s_n).$$ What is the notation for expressing that $S'$ is a (ordered) subsequence of $S$?
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### Elementary question on Sums notation

I reading on Sums and I am reading about the difference between using a generalized Sigma notation and the delimited form. Ok, I understand that the generalized form is more expressive. But I ...
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### Little $o$ notation and series

I have this question: Consider the series $e^{\tan(x)} = 1 + x + \dfrac{x^{2}}{2!} + \dfrac{3x^{3}}{3!} + \dfrac{9x^{4}}{4!} + \ldots$ Retaining three terms in the series, estimate the ...
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