Question

Question 18 Use the sum to infinity of a geometric series to express 0.2222... as a fraction.

Answer 1

Ответ:

ето в англ мову гениальний

Answer 2

To express the repeating decimal 0.2222... as a fraction, you can use the concept of a geometric series. Let's denote the repeating decimal as "x."

x = 0.2222...

Now, notice that if we multiply x by 10, the decimal point will shift one place to the right:

10x = 2.2222...

Now, subtract x from 10x:

10x - x = 2.2222... - 0.2222...

This simplifies to:

9x = 2

Now, divide both sides of the equation by 9 to solve for x:

9x/9 = 2/9

x = 2/9

So, the repeating decimal 0.2222... can be expressed as the fraction 2/9.