Calculus Examples of Geometric Series and More

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

Ramsey 2021-01-31

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

York 2021-01-28

Use the definition of Taylor series to find the Taylor series, centered at c, for the function. $f (x) = \cos x, c = \frac{- π}{4}$

Tammy Todd 2021-01-28

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

Ayaana Buck 2021-01-24

a. Another Maclaurin series we examined is for sin x: a. Find the series for $\frac{\sin (x^{2})}{x}$ . Express the result in the summation notation, not just as a partial listing of the series terms.
b. Another Maclaurin series we examined is for sin x:
d. Find the series for integral $\frac{\sin (x^{2})}{x}$

Reeves 2021-01-22

Find the Maclaurin series for the function $f (x) = \cos 4 x$ . Use the table of power series for elementary functions

snowlovelydayM 2021-01-19

Taylor series
a. Use the definition of a Taylor series to find the first four nonzero terms of the Taylor series for the given function centered at a.
b. Write the power series using summation notation.
$f (x) = 2^{x}, a = 1$

Wribreeminsl 2021-01-19

Find the sum of the series:
$\sum_{n = 0}^{\infty} ((\frac{5}{2^{n}}) - (\frac{1}{3^{n}}))$

alesterp 2021-01-19

Use the Limit Comparison Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \sin \frac{1}{n}$

opatovaL 2021-01-16

Does the series (showing the picture) converge or diverge?
Choose the correct answer below.
1) The integral test shows that the series converges
2) The nth-term test shows that the series converges
3) The series diverges because the series is a geometric series with $| r | >= 1$
4) The nth-term test shows that the series diverges
$\sum_{n = 1}^{\infty} \frac{4^{n}}{n + 1}$

Jaya Legge 2021-01-15

It is important to distinguish between
$\sum_{n = 1}^{\infty} n^{b} and \sum_{n = 1}^{\infty} b^{n}$
What name is given to the first series? To the second? For what values of b does the first series converge? For what values of b does the second series converge?

CheemnCatelvew 2021-01-13

Use the Direct Comparison Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \frac{\sin^{2} n}{n^{3}}$

Daniaal Sanchez 2021-01-13

A) Does this series converge? If yes, towards what number?
B) Find the first 5 terms of the sequence of partial sums in this series.
C) What is the general term of this sequence of partial sums?
$\sum_{k = 1}^{\infty} (\frac{2}{k} - \frac{2}{k + 1})$

Burhan Hopper 2021-01-10

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

a2linetagadaW 2021-01-08

Use a power series to test the series $\sum_{n = 1}^{\infty} n^{\log x}$ for convergence, where $\sum$ means summation

Bergen 2021-01-06

Find a formula for the nth partial sum of the series and use it to determine whether the series converges or diverges. If a series converges, find its sum.
$\sum_{n = 1}^{\infty} (\cos^{- 1} (\frac{1}{n + 1}) - \cos^{- 1} (\frac{1}{n + 2}))$

geduiwelh 2021-01-05

Find the series

shadsiei 2021-01-05

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} 3^{- n}$

CheemnCatelvew 2021-01-04

Using Maclaurin series, determine to exactly what value the following series converges:
$\sum_{n = 0}^{\infty} \frac{(\ln 5)^{n}}{n!}$

Clifland 2021-01-04

Does the attached series converge or diverge? Note: it is a complex series and not a real series. Ive

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