Jul 14, 2003 · A sequence is just that: a sequence of terms that follows a rule of some sort. A series is a summed sequence.

Sep 30, 2020 · A sequence is made up of two sequences a n = (n^2)/ (n+2) - (n^2)/ (n+3) The problem asks for the solver to work out if it's converging or diverging, and find a limit if …

May 31, 2017 · A function is analytic at a point if it can be developed into a power series at this point. This implies it can be extended to a holomorphic function at this point, which means …

Apr 16, 2015 · Homework Equations Divergent series test The Attempt at a Solution i don't understand why 1/k (harmonic series) diverges, when according to the divergent series test, it …

Feb 13, 2010 · The series 1 + 1/8 + 1/27 + 1/64 is identified as a converging series of the form 1/n^3. The integral test confirms convergence as the limit approaches infinity. The main …

Mar 31, 2012 · Let {a_n} converge to a and {b_n} converge to b, then the sequence {a_n+b_n} converges to a+b This is a one way implication. It does not imply that if the sum is convergent …

Mar 28, 2012 · The question is whether the sequence converges, so the answer would be yes or no, right? What question does your book say e/ (e-1) is the answer to? You are correct that the …

Mar 14, 2011 · Looking at the the nth term of e 1/n as n goes to infinity, you see it is equal to 1, which means this series diverges. From the original post, we are dealing with a sequence. So, …

Apr 26, 2012 · The sequence {n/ (n^2+1)} is convergent, with a limit of 0 as n approaches infinity. This conclusion is supported by applying the rules of limits involving infinity, specifically by …

Dec 16, 2008 · A Taylor series is a specific type of power series that is derived from a function to approximate it around a certain point. While all Taylor series are power series, not all power …