Solving Series: Techniques, Examples, and Practice Problems

Power series for derivatives
a. Differentiate the Taylor series centered at 0 for the following functions.
b. Identify the function represented by the differentiated series.
c. Give the interval of convergence of the power series for the derivative.
$f (x) = \ln (1 + x)$

ankarskogC 2021-02-15

Use the formula for the sum of a geometric series to find the sum, or state that the series diverges.
$\frac{7}{8} - \frac{49}{64} + \frac{343}{512} - \frac{2401}{4096} + . . .$

Yulia 2021-02-12

Use the Geometric Series Test to help you find a power series representation of $f (x) = \frac{x}{(2 + x^{3})}$ centered at 0. Find the interval and radius of convergence.

Dillard 2021-02-11

It appears that the terms of the series
$\frac{1}{1000} + \frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + . . .$
are less than the corresponding terms of the convergent series
$1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + . . .$
If the statement above is correct, then the first series converges. Is this correct? Why or why not? Make a statement about how the divergence or convergence of a series is affected by the inclusion or exclusion of the first finite number of terms.

chillywilly12a 2021-02-11

Find a formula for the general term anan (not the partial sum) of the infinite series. Assume the infinite series begins at n=1.
$\frac{2}{1^{2} + 1} + \frac{1}{2^{2} + 1} + \frac{2}{3^{2} + 1} + \frac{1}{4^{2} + 1} + . . .$

naivlingr 2021-02-09

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.
$\frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{9} + \frac{1}{11} + . . .$

Wierzycaz 2021-02-09

Find the sum of the infinite geometric series:
$3 + 2 + \frac{4}{3} + \frac{8}{9} + . . .$

Kaycee Roche 2021-02-08

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.
$\sum_{n = 2}^{\infty} \frac{1}{n \sqrt{\ln n}}$

rocedwrp 2021-02-03

Reasoning as in the given problem, what is the value of
$0.3 + 0.03 + 0.003 + . . . ?$
Working with series Consider the infinite series
$0.9 + 0.09 + 0.009 + 0.0009 + . . .,$
where each term of the sum is $\frac{1}{10}$ of the previous term.
a. Find the sum of the first one, two, three, and four terms of the series.
b. What value would you assign to the infinite series $0.9 + 0.09 + 0.009 +$ ⋅ ⋅ ⋅?

Emeli Hagan 2021-01-22

Find the sum of the infinite geometric series.
$1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + . . .$

Brittney Lord 2021-01-19

The next number in the series 13, 18, 16, 21, 19

Ayaana Buck 2021-01-10

Determine the convergence or divergence of the series.
$\sum_{n = 3}^{\infty} \frac{1}{n (\ln n) [\ln (\ln n)]^{4}}$

opatovaL 2021-01-06

Find the sum of the followinf series. Round to the nearest hundredth if necessary.
$6 + 12 + 24 + \dots + 6144$
Sum of a finite geometric series:
$S_{n} = \frac{a_{1} - a_{1} r^{n}}{1 - r}$

Rui Baldwin 2020-12-14

Write the series and find the sum of the series of sigma notation.
$\sum_{k = 1}^{9} \frac{1}{2^{k}}$

jernplate8 2020-12-13

The next number in the series 3, 4, 6, 7, 9, 10 is: 12 11 15 17 13

glamrockqueen7 2020-12-09

What is the sum of the first six terms of the series?
$40 - 10 + 2.5 - 0.625 + . . .$
What is the answer as a simplified fraction

allhvasstH 2020-12-03

Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges.
$1 - 2 + 4 - 8 + . . . + (- 1)^{n - 1} 2^{n - 1} + . . .$

Aneeka Hunt 2020-11-12

Identify whether the series is an arithmetic series (AS), geometric series (GS) or not one of the difined types ( NASGS ) and determine the sum (for NASGS, write NO SUM). Write your Solution.
a. $1 + \frac{3}{2} + \frac{9}{4} + . . . + \frac{81}{16}$

beljuA 2020-11-08

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.
$\sum_{n = 1}^{\infty} \frac{\arctan n}{n^{2} + 1}$

Cabiolab 2020-10-18

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.
$\sum_{n = 1}^{\infty} \frac{1}{{(2 n + 3)}^{3}}$

Series math problems relate to the precalculus stage of mathematical studies that are met both by high school students and college learners dealing with analysis. The questions that are brought up by this specific approach will include solving series equations that represent the sum of a sequence to a certain number of terms. You can take a look at various series math examples that will help you approach series math questions that may relate either to statistical calculations or engineering equations that are mostly used in engineering and data programming.

Precalculus

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