Calculus Examples of Geometric Series and More

Why is $lim_{n \to \infty} {(\frac{n - 1}{n + 1})}^{2 n + 4} = \frac{1}{e^{4}}$

Kayden Mills 2022-11-02

Find $A = \sum_{n = 1}^{\infty} \frac{\log 2^{n}}{3^{n}}$

Aryanna Fisher 2022-11-02

Find the limit of $x_{n} = \prod_{j = 2}^{n} {(1 - \frac{2}{j (j + 1)})}^{2}$

Christopher Saunders 2022-11-01

Proving convergence of a series
$\tanh \frac{1}{n} + \ln \frac{n^{2} - n}{n^{2} + 1}$

Angel Kline 2022-10-31

Explicit formula for the series $\sum_{k = 1}^{\infty} \frac{x^{k}}{k! \cdot k}$

Paloma Sanford 2022-10-24

Use the principle of mathematical induction to prove the following formula.
$\sum_{j = 0}^{n} j^{3} = \frac{n^{2} (n + 1)^{2}}{4}$

Antwan Perez 2022-10-20

Find the sum:
$\sum_{k = 3}^{6} (k^{2} - 7)$

clasicaacyx 2022-09-17

Two number have a sum of 124 and a difference of 46. Find the humbers

Kailey Vargas 2022-09-09

Find the sum of the first 85 terms of the arithmetic series.
$33 + 40 + 47 + 54 + . . .$

Zackary Duffy 2022-09-06

The coefficient of $x^{6}$ in the Maclaurin series expansion of $f (x) = (1 + 4 x^{2})^{- \frac{2}{5}}$ is?

reinzogoq 2022-09-03

Find series:
$\sum_{k = 1}^{n} (3 + 4 k)^{2}$

imire37 2022-08-05

There are various types of numbers, including the following types: Odd Even Whole Natural Integer Rational Irrational Real a) Order these types in terms of how one type can be included in another. You may draw a diagram, graph or table to explain the relationships. b) Give at least one example of each type of number. The example should be specific. Choose an example that, ideally, could not be assigned to any more limited or restricted type. c) Give at least two examples of how operations (such as addition) on numbers belonging to one type can produce a result that belongs to another type.

Flambergru 2022-08-02

The sum to infinity of a G.P series is R.
The sum to infinity of the squares of the terms is 2R.
The sum to infinity of the cubes of the terms is (64/13)R.
Find (i) the value of R. (ii) the first term of the first original series.

abrham enyew2022-07-29

$f (x) = \sqrt[3]{x^{3}}$

vangstosiis 2022-07-29

Find the sum of the series.
$\sum_{n = 1}^{\infty} \frac{7}{4^{n}}$

skynugurq7 2022-07-16

$\frac{1}{2 \cdot 4} + \frac{1 \cdot 3}{2 \cdot 4 \cdot 6} + \frac{1 \cdot 3 \cdot 5}{2 \cdot 4 \cdot 6 \cdot 8} + \frac{1 \cdot 3 \cdot 5 \cdot 7}{2 \cdot 4 \cdot 6 \cdot 8 \cdot 10} + \dots$
is equal to?

vasorasy8 2022-07-14

How do I evaluate $\sum_{n = 1}^{\infty} \frac{(- 1)^{n + 1} H_{n}}{2 n + 1} ?$

Esmeralda Lane 2022-07-14

Determine the convergence of $\sum_{n = 2}^{\infty} \sin (n π + \frac{1}{\ln n})$

auto23652im 2022-07-14

The sequence $(b)_{n \geq 0}$ shall satisfy
$b_{n} = \sum_{k = 0}^{n} (\binom{n}{k}) a_{k}$

Holetaug 2022-07-14

Why the limit of the following sequence is like this:
$\frac{2 \sqrt[n]{n!}}{n} = \frac{2}{e}$

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