Question

Which geometric series represents 0.4444... as a fraction? one-fourth startfraction 1 over 40 endfraction startfraction 1 over 400 endfraction startfraction 1 over 4,000 endfraction ellipsis startfraction 1 over 40 endfraction startfraction 1 over 400 endfraction startfraction 1 over 4,000 endfraction startfraction 1 over 40,000 endfraction ellipsis four-tenths startfraction 4 over 100 endfraction startfraction 4 over 1,000 endfraction startfraction 4 over 10,000 endfraction ellipsis one-tenth startfraction 1 over 100 endfraction startfraction 1 over 1,000 endfraction startfraction 1 over 10,000 endfraction ellipsis

Answer 1

The geometric series which represent the provided number in the fraction form is,

$\dfrac{4}{10}, \dfrac{4}{100},\dfrac{4}{1000},\dfrac{4}{10,000}$

What is geometric sequence?

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

The fraction number given in the problem is,

$n=0.4444.....$

Let's break the given number into the parts as,

$n=0.4+0.04+0.004+0.0004+.....$

The decimal number 0.4 is written as 4/10. Similarly, 0.04 can be written as 4/100. Thus, the above number can also be written as,

$n=\dfrac{4}{10}+\dfrac{4}{100}+\dfrac{4}{1000}+\dfrac{4}{10,000}+\cdots$

Hence, the geometric series which represent the provided number in the fraction form is,

$\dfrac{4}{10}, \dfrac{4}{100},\dfrac{4}{1000},\dfrac{4}{10,000}$

Learn more about the geometric sequence here;

https://brainly.com/question/1509142