![]() ![]() but this does not make sense, since the series shouldn't converge. A series however is the SUM of a sequence or progression. Or 1, 2, 4, 8, 16, which is a geometric sequence. For example 2,4,6,8,10 is an (arithmetic) sequence. Remember that a sequence is like a list of numbers, while a series is a sum of that list. Progession and sequence are the same thing a list of numbers generated according to some rule or rules. sequences and series answers Sequences and series Algebra 2 (LBUSD pilot) - Khan Academy. but surely we need an implicit reason that this works for some numbers, and not others? The way it is written, is that the second equations huge number should cancel out the same huge number in the first equation, and we will be left with an a. I think you are confusing sequences with series. ![]() it just is, because Sal says so! is this because we are dealing with with infinity? but what is the reason r is limited in the values it can take on.? it isn't implicit in the derivation. I realise the denominator becomes a negative, and this doesn't necessarily make sense. In the first video, if every a in the first equation gets cancelled out by an a in the second equation (assuming this is true for infinity, since both equations go to infinity) except for the initial ar^0, how does this formula not work for r>1? In addition, a sequence can be thought of as an ordered list.
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