What is the sum of the infinite geometric sequence
0.2+0.0.2+0.002+...

In decimal form, this approximately 0.2222

Explanation:

The first term is a = 0.2

The common ratio is r = 0.1

Note how

Which helps show we have the correct r value.

Because -1 < r < 1 is true, this means the infinite geometric sum converges.

The sum converges to

S = a/(1-r)

S = 0.2/(1-0.1)

S = 0.2/0.9

S = 2/9 exactly

S = 0.2222 approximately

Note how the 2's go on forever in the decimal version of 2/9. This matches with the fact that each new term added on effectively adds on a new digit of 2

In other words,

And so on.

answer is : muchas/tipicas

have a nice day!

~recklesschicken