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Hurkyl

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Why would you think that?if two rational numbers added together is still rational then wouldn't an infinite sume of rational numbers that converge also be rational

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no this can easily be seen by looking at .101001000100001... this number is actually transcendental but it’s power series representation has nothing but rational terms i.e.if two rational numbers added together is still rational then wouldn't an infinite sume of rational numbers that converge also be rational

1/10 + 1/10^3 + 1/10^6 + 1/10^10 + 1/10^15…

Just because something intuitively seems it should be a certain way in math doesn’t mean it is. Math is about what you can deduce logically, not what you feel something should be like.

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HallsofIvy

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For example, [itex]\pi[/itex]= 3+ 0.1+ 0.04+ 0.001+ 0.0005+ 0.00009+ 0.000002+ ...

Why would you think that what is true for a finite sum is necessairly true for an infinite sum?

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infinite sum is just a simple notation of writing sum to n where n -> inf.

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thanks for all your help i just wanted to clarify that for myself

- #8

HallsofIvy

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For an infinite series, the limit of the partial sums

infinite sum is just a simple notation of writing sum to n where n -> inf.