How would I do this the fraction way, I want to get used to doing it in fraction form, that would make things much easier.

2. 5 - 1 + 1/5 -...

Common ratio is -0.2, so that would be -1/5.

S = a/1-r
S = 5/1-(-0.2)
S = 5/1.2 = 4.166 = 25/6

S∞ = 5/(1-(-1/5))

=5/(1 + 1/5)
= 5/(6/5)
= 5(5/6) = 25/6

Thanks so very much :)

To solve the given series using fractions, we can convert the decimal values to fractions and then apply the formula for the sum of an infinite geometric series.

The given series is 5 - 1 + 1/5 - ...

First, let's find the common ratio. As you correctly identified, the common ratio is -1/5.

Next, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Here, 'a' represents the first term of the series, and 'r' represents the common ratio.

So, plugging in the values:

S = 5 / (1 - (-1/5))

Simplifying the denominator:

S = 5 / (1 + 1/5)

Finding a common denominator:

S = 5 / (5/5 + 1/5)

S = 5 / (6/5)

Invert and multiply:

S = 5 * (5/6)

S = 25/6

Therefore, the sum of the series is 25/6 or 4.166.