r/askmath • u/Equivalent_Dingo_683 • 9d ago

Discrete Math Simplify sum

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Friend gave this "easy" sum for Olympiad practice, can't solve it even though I already tried relating it to e's Taylor series done harmonic stuff etc, any help?

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u/uTRexAap 9d ago

havent taken any calc so im terrible at this but i got it down to this

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u/BubbhaJebus 6d ago

Then reindex it.

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u/uTRexAap 6d ago

What does that mean?

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u/BubbhaJebus 6d ago

Rewrite it so the index of summation ranges from 1 to n-1 instead of 2 to n. It's a little simpler that way.

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u/uTRexAap 6d ago

You can do that???????

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u/BubbhaJebus 6d ago

Yes: SUM(i = 2 to n) f(n) = SUM(i = 1 to n-1) f(n+1)

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u/uTRexAap 6d ago

At that point why not 0 to n-2 ?