Using geometric progression express 5.666666666 as a fraction

2 answers

We can represent 5.666666666 recurring as an infinite geometric progression with first term 5 and common ratio 1/10:

5 + 0.6 + 0.06 + 0.006 + ...

To find the sum of an infinite geometric progression, we use the formula:

S = a/(1-r)

where S is the sum of the progression, a is the first term, and r is the common ratio.

In this case, we have:

S = 5/(1-1/10) = 5/(9/10) = 50/9

Therefore, 5.666666666 recurring can be expressed as a fraction:

5.666666666 = 50/9
AAAaannndd the bot gets it wrong yet again!
5 is not part of the sequence.

.6666 = a/(1-r) = 0.6/(1 - 0.1) = 0.6/0.9 = 2/3
5.666666666 = 5 2/3 = 17/3