Calculus Examples of Geometric Series and More

Determine the sum of the following series.
$\sum_{n = 1}^{\infty} (\frac{1^{n} + 9^{n}}{11^{n}})$

Tomasettiq3 2021-11-13

Use linear approximation (or differentials) to estimate:
$\sqrt{99.2}$
What am I supposed to do with this? I am not given x or dx

veudeje 2021-11-13

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A circular swimming pool has a diameter of 24 ft, the sides are 5 ft high, and the depth of the water is 4 ft. How much work is required to pump all of the water out over the side? (Use the fact that water weighs 62.5lb/ft^3.)

gabioskay7 2021-11-13

Compute each of these double sums:
a) $\sum_{i = 1}^{2} \sum_{i + 1}^{3} (i + j)$
b) $= \sum_{i = 1}^{2} (i + 1 + i + 2 + j + 3)$

glamrockqueen7 2021-11-08

Approximate the sum of the series correct to four decimal places.
$\sum_{n}^{\infty} n = \frac{1 {(- 1)}^{n}}{3^{n} n!}$

Globokim8 2021-11-05

Express the definite integral as an infinite series and find its value to within an error of at most
$10^{- 4}$
$\int_{0}^{1} \cos (x^{2}) d x$

Jason Farmer 2021-11-04

Prove that $1 \cdot 1! + 2 \cdot 2! + \cdot \cdot \cdot + n \cdot n! = (n + 1)! - 1$ whenever n is a positive integer.

nicekikah 2021-11-03

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 3-4+16/3-64/9+........

Maiclubk 2021-11-03

Find a power series for the function, centered at c, and determine the interval of convergence.
$g (x) = \frac{3}{2 x - 1}, c = 2$

vazelinahS 2021-11-02

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
$10 - 2 + 0.4 - 0.008 + \dots$

ossidianaZ 2021-10-25

Determine the interval of convergence and find a power series representation for the function.
$f (x) = \frac{2}{3} - x$

Lipossig 2021-10-24

Test the series for convergence or divergence.
$\sum_{n = 0}^{\infty} \frac{{(- 1)}^{n + 1}}{\sqrt{n + 4}}$

lwfrgin 2021-10-22

Using only the definition of Riemann sum and your knowledge of limits, compute the exact area under the curve $2 x^{2}$ between x=-2 and x=1.

Anish Buchanan 2021-10-19

What is the probability that a five-card poker hand contains cards of five different kinds?

illusiia 2021-10-19

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that $R n (x) \to 0$ .] Also find the associated radius of convergence. $f (x) = 2^{x}$

Falak Kinney 2021-10-18

A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. Hint: Let $E_{n}$ denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n-1 rolls. Compute $P (E_{n})$ and argue that $\sum_{n = 1}^{\infty} P (E_{n})$ is the desired probability.

Harlen Pritchard 2021-10-17

A pair of honest dice is rolled once. Find the expected value of the sum of the two numbers rolled.

vestirme4 2021-09-06

$\sum_{x = 1}^{\infty} \frac{1}{8^{n}}$

opatovaL 2021-09-04

Simplify $(\sec θ - \tan θ) (1 + \sin θ)$

sjeikdom0 2021-09-03

$\sum_{x = 1}^{\infty} \frac{n + 6}{n^{2} + 12 n + 8}$

The majority of questions about series calculus that you will find online will have odd solutions that do not really provide explanations or the answers that would help one understand how things work. We have taken a different approach by offering series calculus practice questions that are connected with initial equations that must be solved. It is once again about estimation and analysis as the examples include the building of the bridges and calculation of the power or energy necessary to implement the safest solution by estimating the best one. By offering clear examples, we help you learn things easier!

Calculus 2

Calculus Series: Understanding Geometric Examples