Calculus Examples of Geometric Series and More

Find the sum of the infinite geometric series.
$\sum_{i = 1}^{\infty} 12 (- 0.7)^{i - 1}$

slaggingV 2021-02-06

a. Find an upper bound for the remainder in terms of n.
b. Find how many terms are needed to ensure that the remainder is less than $10^{- 3}$ .
c. Find lower and upper bounds (ln and Un, respectively) on the exact value of the series.
$\sum_{k = 1}^{\infty} \frac{1}{3^{k}}$

floymdiT 2021-02-06

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

Dottie Parra 2021-02-05

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

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.
$\sum_{k = 1}^{\infty} 10^{k}$

Tobias Ali 2021-02-05

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

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 $\frac{1}{\sqrt{3}}$

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 $\cos (- 2 x)$

aflacatn 2021-02-04

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

slaggingV 2021-02-04

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

bobbie71G 2021-02-03

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

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.

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:
$\cos (x) = \sum_{n = 0}^{\infty} (- 1)^{n} \frac{x^{2 n}}{(2 n)!} = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} + \frac{x^{8}}{8!} - \frac{x^{10}}{10!} + . . .$

midtlinjeg 2021-02-02

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

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.
$\sum_{n = 2}^{\infty} \frac{7 \cdot (- 3)^{n}}{5^{n}}$

UkusakazaL 2021-01-31

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

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