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Coda · Posted 04-07-2017, 06:54 PM

It's multiplied by a₁ because k⁰ = 1.

That's one way to start from 0, yes. It's far from the ONLY way. In fact it's usually easier to start from 0 once you wrap your head around the idea. The n(n+1) works fine from 0 as it is because 0(0+1) = 0; we can clearly see that the sum of 0..n for n=0 is (drumroll please) 0.

Coda Developer			#311
	It's multiplied by a₁ because k⁰ = 1. That's one way to start from 0, yes. It's far from the ONLY way. In fact it's usually easier to start from 0 once you wrap your head around the idea. The n(n+1) works fine from 0 as it is because 0(0+1) = 0; we can clearly see that the sum of 0..n for n=0 is (drumroll please) 0. Games by Coda (updated 4/8/2025 - New game: Marianas Miner) Art by Coda (updated 8/25/2022 - beatBitten and All-Nighter Simulator) Mega Man: The Light of Will (Mega Man / Green Lantern crossover: In the lead-up to the events of Mega Man 2, Dr. Wily has discovered emotional light technology. How will his creations change how humankind thinks about artificial intelligence? Sadly abandoned. Sufficient Velocity x-post)
		Posted 04-07-2017, 06:54 PM