Infinite Sequences and Series (BC Only)

For what value of $k$ does the infinite series $\sum_{n=2}^{\infty} \frac{k^n}{\ln(n)}$ converge using the Root Test?

If a function's seventh-degree Maclaurin polynomial is used to estimate $\int_0^1 f(x),dx$, which choice best approximates how many times more accurate this estimate would be compared to using its third-degree Maclaurin polynomial given that both functions have continuous derivatives up to eighth order on [0,1]?

What is the name of Taylor Series centered at x=0?

What is the third-degree Taylor polynomial about $x = 0$ for the function $f(x) = e^x$?

Using L'Hôpital's Rule, what limit comparison could you use to determine whether a function has a finite non-zero radius convergence when expanded as a power series around $x=0$?

For a function whose third derivative is always negative, how does constructing its second-degree Taylor polynomial about $x = c$ affect its estimation errors for values $x > c$?

If a function's sixth-degree Maclaurin polynomial is used instead of its third-degree counterpart to predict values around zero, how many more initial derivatives compared to the third degree must be precisely calculated on an interval containing zero to guarantee an improved estimate within this range?

What is the radius of convergence for the power series $\sum_{n=0}^{\infty}\left(\frac{n+3}{2^{n}}\right)(x-4)^n$ centered at x =4?

If the series $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}(5^n)}{n!}$ converges, to which of the following values does it approximate closest?

The fifth term ($a_5$) in an arithmetic sequence characterized by having its first three terms as $6, 8, 10$ would be what value?