convert the decimal 0.6 to a fraction by writing it as a infinite series.
I really have no idea how to do this can anyone please help me?
what is the sum of
.30 + .15+ .075+.0375 + .01875+ .009375+ ...
Sum .30/2^n n=0,1,2,3,4,,,,,,,to inf
2.25
To convert the decimal 0.6 to a fraction using an infinite series, we can express it as a sum of fractions with increasing denominators.
First, let's write 0.6 as a fraction with a denominator of 1:
0.6 = 0.6/1
Next, we need to express the fraction with a denominator of 1 as a sum of fractions with denominators increasing by powers of 10. So, we'll start by multiplying both the numerator and denominator by 10:
0.6 = (0.6 × 10) / (1 × 10) = 6/10
Now, let's simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2 in this case:
6/10 = (6 ÷ 2) / (10 ÷ 2) = 3/5
So, the decimal 0.6 can be expressed as the infinite series 3/5.
Please note that this process of expressing a decimal as an infinite series may not work for all decimal numbers.