Jan 9, 2017 · The problem is that the sequence you consider doesn't converge. In the extended real numbers, it is a divergent sequence with two limit points: $0$ and $+\infty$. In that regard, it's …

Oct 19, 2016 · Also, this illustrates why we care about rigorous definitions in math. Once we've defined what a sequence is, what convergence means, etc., this isn't a philosophical question; it has a …

Mar 22, 2024 · Does sequence mean repition? No, sequence does not inherently mean repetition. A sequence refers to an ordered arrangement of elements, which can be distinct or repeated.

1 This problem is a direct application of Dirichlet's test for series convergence. Note that, since the sequence $ (a_n)$ converges, then the sequence of partial sums is bounded.

Feb 21, 2015 · In other words, your teacher's definition does not say that a sequence is bounded if every bound is positive, but if it has a positive bound. The sequence $ (0,0,\ldots)$ has indeed a positive …

Mar 25, 2015 · I know of the monotone convergence theorem, but does this mean that sequences converge only if they are bounded and monotone?

What does ! mean in sequences? Ask Question Asked 13 years, 8 months ago Modified 9 years, 7 months ago

Apr 21, 2021 · For the sequential definition, I think it'll actually be more helpful to picture not a sequence of inputs and a sequence of outputs seperately, but rather the sequence $\left (x_n, f (x_n)\right)_ {n …

Nov 7, 2015 · From wikipedia, we have the definition of a sequence to be "a sequence is an ordered collection of objects in which repetitions are allowed." But I don't understand the meaning of …

Aug 25, 2019 · Show that $ (c_n)$ is a " zero-sequence " if and only if both $ (a_n)$ and $ (b_n)$ are " zero-sequences ". Can someone please explain with words what the definition of a " zero-sequence " …