Detailed Explanations for Calculus 2 Equations

Find the values of x for which the given geometric series converges. Also, find the sum of the series (as a function of x) for those values of x.
a) Find the values of x for which the given geometric series converges.
b) Find the sum of the series
$\sum_{n = 0}^{\infty} (- \frac{1}{2})^{n} (x - 5)^{n}$

Daniaal Sanchez 2020-11-08

Find the sum of the convergent series.
$\sum_{n = 1}^{\infty} \frac{4}{n (n + 2)}$

Alyce Wilkinson 2020-11-08

Determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \frac{n}{\sqrt{3 n^{2} + 3}}$

Falak Kinney 2020-11-08

Find the first 7 terms for the Taylor Series at 0
$f (x) = \frac{1}{\sqrt{1 + x}}$
Make a substitution in the above taylore series to get the first 7 terms for the Taylor Series
$f (x) = \frac{1}{\sqrt{1 - x}}$

Chesley 2020-11-08

Use the Limit Comparison Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \frac{n^{k - 1}}{n^{k} + 1}, k > 2$

allhvasstH 2020-11-08

Find the radius of convergence and interval of convergence of the series.
$\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n} 10^{n} x^{n}}{n^{4}}$

vazelinahS 2020-11-08

Consider the following infinite series.
a.Find the first four partial sums $S_{1}, S_{2}, S_{3},$ and $S_{4}$ of the series.
b.Find a formula for the nth partial sum $S_{n}$ of the indinite series.Use this formula to find the next four partial sums $S_{5}, S_{6}, S_{7}$ and $S_{8}$ of the infinite series.
c.Make a conjecture for the value of the series.
$\sum_{k = 1}^{\infty} \frac{2}{(2 k - 1) (2 k + 1)}$

vestirme4 2020-11-06

Determine the convergence or divergence of the series.
$\sum_{n = 2}^{\infty} \frac{1}{n (\ln n)^{3}}$

Clifland 2020-11-05

Use ana appropriate test to determine whether the series converges.
$\sum_{k = 1}^{\infty} (\frac{k!}{20^{k} k^{k}})$

Kyran Hudson 2020-11-02

Use the alternating series test to determine the convergence of the series
$\sum_{n = 1}^{\infty} (- 1)^{n} \sin^{2} n$

waigaK 2020-11-01

Find the gradient at the point (3, -3, 2) of the scaler field given by $= - 4 + 35$

sjeikdom0 2020-11-01

Find the interval of convergence of the power series, where c > 0 and k is a positive integer.
$\sum_{n = 1}^{\infty} \frac{n! {(x - c)}^{n}}{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2 n - 1)}$

CoormaBak9 2020-10-28

Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series.
$f (x) = \ln \sqrt{4 - x}$

babeeb0oL 2020-10-28

Which of the series, and which diverge?
Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)
$\sum_{n = 1}^{\infty} \frac{1}{2 n - 1}$

Amari Flowers 2020-10-27

Find the interval of convergence of the power series.
$\sum_{n = 1}^{\infty} \frac{(- 1)^{n} x^{n}}{n}$

Maiclubk 2020-10-27

Which of the series, and which diverge?
Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)
$\sum_{n = 1}^{\infty} \frac{3}{\sqrt{n}}$

Josalynn 2020-10-26

Discuss the convergence of the following series:
$\sum_{n = 1}^{\infty} \frac{\cos n π}{n^{2} + 1}$

slaggingV 2020-10-26

For each of the following series, using no tests besides the nth Term and Comparison Tests, determine whether the series converges, diverges to $\pm \infty$ , or diverges, not to $\pm \infty$
$\sum \frac{n - 1}{n^{2} - 1}$

slaggingV 2020-10-26

Expand $\frac{1}{\sqrt[4]{1 + x}}$ as a power series

generals336 2020-10-25

Determine whether the given series is convergent or divergent. Explain your answer. If the series is convergent, find its sum.
$\sum_{n = 0}^{\infty} \frac{3^{n} + 2^{n + 1}}{4^{n}}$

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