1.Write the equation of the circle with a center at (-6, 1) and an area of 7π.

Solved

Show answers

Ответ:

nsuleban5016

02.08.2021

Mathematics

OPTION B

Step-by-step explanation:

Geometric series : $\displaystyle \sum_{n = 0}^{ \infty} ar^n$

where is the first term of the series and

is common difference.

A geometric series is convergent if |r| < 1.

It is divergent otherwise.

Since the first term of the series is a and the second term is ar, the ration of second term and first term, $\frac{ar}{r}$ = r.

OPTION A:

$\frac{1}{81} + \frac{1}{27} + \frac{1}{9} + \frac{1}{3} + \hdots$ .

Here, $a = \frac{1}{81}$ and $ar = \frac{1}{27}$

$\implies r= \frac{27}{81} = 3$

r > 1. So, this series is divergent.

OPTION B:

$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \hdots$

a = 1; ar = $\frac{1}{2}$ .

$\implies r = \frac{1}{2}$ .

Since, r < 1, we can say that the series is convergent.

OPTION C:

We can easily see that |r| =4. So, it is not convergent.

OPTION D:

Again |r| = 2. So, the series should be divergent.

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice