How can an convergent series of rational numbers result in a irrational number?

Emmy Dillon
2022-06-24
Answered

How can an convergent series of rational numbers result in a irrational number?

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Esteban Johnson

Answered 2022-06-25
Author has **15** answers

Adding any two rational numbers results in a rational number. By induction, adding any finite number of rational numbers together results in a rational number.

Adding together infinitely many rational numbers has no such guarantee, in exactly the same way that there is no guarantee that such a sum is finite.

Adding together infinitely many rational numbers has no such guarantee, in exactly the same way that there is no guarantee that such a sum is finite.

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Suppose $\sqrt{2}$ is an irrational number and $0$ is a rational number. Because

$\sqrt{2}=\sqrt{2}+0$

the sum of an irrational number and a rational number is an irrational number.

Is this correct?

$\sqrt{2}=\sqrt{2}+0$

the sum of an irrational number and a rational number is an irrational number.

Is this correct?

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