1/19/2024 0 Comments Khan academy sequences and serieswe're going to start at one and just increment by one one, two, three and we're going to go all the way to n And what I want to think about is what is the sum of this sequence going to be? And the sum of a sequence, we already know we call a series so what is the sum and I will just call it Sn what is this going to be equal to one plus two plus three plus going all the way to n well, we're going to do a neat little trick here where I'm going to rewrite this sum so I will write it again as Sn but now I'm just going to write it in reverse order I'm going to write it as n plus n minus one plus n minus two all the way to one and now I'm going to add these two equations So we know that Sn is equal to this so we are adding the same thing to both sides of this equation up here So on the left hand side we're going to have Sn plus Sn is just two times Sn and on the right hand side and this is where we start to see something kind of cool you have a one plus an n which is just going to be n plus one you have a two plus n minus one which is. Let's say we have the simplest of arithmetic sequences and probably the simplest of sequences one, two.
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