Look at the following sum. 1 + 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64. . . Notice that the denominator of each fraction in the sum is twice the denominator that comes before it. If you continue adding on fractions according to this pattern, when will you reach a sum of 2?

No matter how long you continue to add this sequence of fractions, you can never reach a sum of 2, although your answer gets closer to 2 each time you add a fraction.

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abidemiokin abidemiokin · Answer 2 · 2021-10-12T12:46:09+02:00

If you continue adding on fractions according to this pattern, we will reach the value of 2

Given the series of numbers 1 + 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64..., we can see that the sum of the numbers tends to infinity.

In order to know if whether we will reach a sum of 2, if we keep adding the fraction, we will find the sum to infinity of the sequence:

The sum to infinity of a geometric sequence is expressed as:

[tex]S_n=\frac{a}{1-r}[/tex]

s is the first term

r is the common ratio

From the given sequence:

a = 1

r = [tex]\frac{1/2}{1} = \frac{1/4}{1/2}=\frac{1}{2}[/tex]

Substitute the given parameters into the formula as shown:

[tex]S_\infty=\frac{1}{1-\frac{1}{2} }\\S_\infty=\frac{1}{1/2}\\S_\infty = 2[/tex]

This shows that if you continue adding on fractions according to this pattern, we will reach the value of 2

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