Detailed Explanations for Calculus 2 Equations

Which series converge, and which diverge?If a series converges, find its sum.
$\sum_{n = 0}^{\infty} (\ln (4 e^{n} - 1) - \ln (2 e^{n} + 1))$

Tobias Ali 2021-02-05

Find the sum of the following series
$\sum_{k = 2}^{\infty} (- 1)^{k} \frac{3}{2^{3 k}}$

Jason Farmer 2021-02-05

The terms of a series are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning.
$\sum_{n = 1}^{\infty} a_{n}$
$a_{1} = \frac{1}{5}, a_{n + 1} = \frac{\cos n + 1}{n} a_{n}$

Alyce Wilkinson 2021-02-05

For the following infinite series, find the first four terms of the sequence of partial sums. Then make a conjecture about the value of the infinite series or state that the series diverges.
$\sum_{k = 1}^{\infty} 10^{k}$

Dottie Parra 2021-02-05

Determine the radius and interval of convergence of the following power series.
$\sum_{k = 0}^{\infty} (2 x)^{k}$

Falak Kinney 2021-02-05

Approximating powers Compute the coefficients for the Taylor series for the following functions about the given point a, and then use the first four terms of the series to approximate the given number.
$f (x) = \frac{1}{\sqrt{x}}$ with $a = 4$ , approximate $\frac{1}{\sqrt{3}}$

slaggingV 2021-02-04

Use a Maclaurin series in this table (attached) toobtain the Maclaurin series for the given function.
$f (x) = 5 \cos (\frac{π x}{8})$

aflacatn 2021-02-04

Evaluate the following limits using Taylor series.
$lim_{x \to 0} \frac{\tan^{- 1} x - x}{x^{3}}$

boitshupoO 2021-02-04

Calculate the following:
a. Find the Maclaurin series of $\cos (x)$ and find the radius of this series, without using any known power or Maclaurin series, besides geometric.
b. Find exactly the series of $\cos (- 2 x)$

postillan4 2021-02-03

Given the series:
$9 + \frac{117}{4} + \frac{1521}{16} + \frac{19773}{64} + . . .$
does this series converge or diverge? If the series converges, find the sum of the series.

bobbie71G 2021-02-03

Find the interval of convergence of the power series.
$\sum_{n = 0}^{\infty} \frac{(3 x)^{n}}{(2 n)!}$

midtlinjeg 2021-02-02

Which series converge, and which diverge? Give reasons for your answers. If a series converges, find its sum.
$\sum_{n = 1}^{\infty} \frac{2}{10^{n}}$

Marvin Mccormick 2021-02-02

Use the alternating series test to study the convergence of the following series
$\sum_{n = 1}^{\infty} (- 1)^{n + 1} n e^{- n}$

aortiH 2021-02-02

Find the Maclaurin series for $f (x) = x^{4} \cos x$ . Also, find the third term for this series.
The Maclaurin series for $\cos (x)$ is given by:
$\cos (x) = \sum_{n = 0}^{\infty} (- 1)^{n} \frac{x^{2 n}}{(2 n)!} = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} + \frac{x^{8}}{8!} - \frac{x^{10}}{10!} + . . .$

Khadija Wells 2021-02-01

Represent the function $3 \ln (8 - x)$ as a power series
What is the radius of convergence?

Wierzycaz 2021-01-31

Given the geometric series $\sum_{n = 2}^{\infty} \frac{7 (3)^{n}}{(- 5)^{n}}$
a) Find r, the common ratio.
b) Determine if the series converges or diverges.
c) If it converges, find the limit.

he298c 2021-01-31

Use the formula for the sum of a geometric series to find the sum, or state that the series diverges.
$\sum_{n = 2}^{\infty} \frac{7 \cdot (- 3)^{n}}{5^{n}}$

Ramsey 2021-01-31

We need to find the sum of the given series.
$\sum_{n = 4}^{\infty} (\frac{1}{n + 1} - \frac{1}{n + 2})$

sodni3 2021-01-31

Use the formula for the sum of a geometric series to find the sum, or state that the series diverges.
$\sum_{n = 0}^{\infty} \frac{3 (- 2)^{n} - 5^{n}}{8^{n}}$

UkusakazaL 2021-01-31

Use the Limit Comparison Test to prove convergence or divergence of the infinite series.
$\sum_{n = 2}^{\infty} \frac{n}{\sqrt{n^{3} + 1}}$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More