Infinite Sequences and Series (BC Only)

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?

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

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

Which term is included in the second-degree Taylor polynomial for the function f(x) at x = a?

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