Problem 1
Use your own words to describe how sequences and series are related.
Problem 1
Use your own words to define a sequence.
Problem 1
What is the difference between a Taylor polynomial and a Taylor series?
Problem 1
Why is \(\sum_{n=1}^{\infty} \sin n\) not an alternating series?
Problem 2
A series \(\sum_{n=1}^{\infty}(-1)^{n} a_{n}\) converges when \(\left\\{a_{n}\right\\}\) is _____, ______ and \(\lim _{n \rightarrow \infty} a_{n}=\underline{ }\)_____.
Problem 2
Use your own words to define a partial sum.
Problem 2
What theorem must we use to show that a function is equal to its Taylor series?
Problem 2
What is the difference between the radius of convergence and the interval of convergence?
Problem 3
What three convergence tests do not work well with terms containing factorials?
Problem 3
Give an example of a series where \(\sum_{n=0} a_{n}\) converges but \(\sum_{n=0}^{\infty}\left|a_{n}\right|\) does not.
