How can adding an infinite number of rationals yield an

Semaj Christian

Semaj Christian

Answered question

2022-06-17

How can adding an infinite number of rationals yield an irrational number?

Answer & Explanation

Elianna Douglas

Elianna Douglas

Beginner2022-06-18Added 23 answers

For example
π = 3 + 0.1 + 0.04 + 0.001 + 0.0005 + 0.00009 + 0.000002 +
Hailie Blevins

Hailie Blevins

Beginner2022-06-19Added 8 answers

You can't add an infinite number of rational numbers. What you can do, though, is find a limit of a sequence of partial sums. So, π 2 / 6 is the limit to infinity of the sequence 1 , 1 + 1 / 4 , 1 + 1 / 4 + 1 / 9 , 1 + 1 / 4 + 1 / 9 + 1 / 16 , Writing it so that it looks like a sum is really just a shorthand.

In other words, i = 1 is actually kind of an abbreviation for lim n i = 1 n .

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