Infinite Sequences and Series (BC Only)

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?

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 $x > c$?

What is the first term ($a_1$) of the geometric series represented by $\sum_{n=0}^{\infty} \frac{5}{2^n}$?

Given that the fifth-degree Taylor polynomial for $f(x) = e^{2x}$ centered at $x=0$ is used to approximate $f(0.1)$, which of the following values most closely represents the absolute error of this approximation?

What is the primary purpose of using Taylor polynomial approximations?

What does the expression $\sum_{n=0}^\infty \dfrac{f^{(n)}(a)}{n!}(x-a)^n$ represent?

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?

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?

What is the third-degree Taylor polynomial approximation of $f(x) = e^x$ centered at $x=0$?