Good to get a sense that, you know, that this formula Videos, we have proved this formula, but it's always And there is a formula for the sum of an arithmetic series, andįirst we're just going to apply the formula, but then we're going to getĪ little bit of an intuitive sense for why that formula works, and actually, in other We are increasing by the same amount each time. We can recognize this as an arithmetic series. Term, we're increasing by the same amount, we're increasing by 2, we're increasing by 2, The sum of all of these, and since each successive We're just going to keep adding 2 for each successive term, all the way until we get to 1150, and we're going to take So that gives us a good feel for this sum, for this series.
Sigma notation examples plus#
This first term is going to be, it evalutes to 52 plus, this next term is 2 times 2 plus 50 is going to be 54, plus the next term, 2 times 3 is 6 plus 50 is 56, and we're going to go all the way, all the way to our last term, 2 times 550 is 1100 plus 50 is going to be 1150.
Going all the way until we get to the last term, when k is equal to 550, it's going to be 2 times 550 plus 50. When k is equal to 3, it's going to be 2 times 3 plus 50. When k is equal to 2, it's going to be 2 times 2 plus 50.
This is going to look like, when k is equal 1, this is going to be 2 times 1 plus 50. Out the sum a little bit just so that I can get aįeel for what it looks like, so let's see. So this is a sum from kĮquals 1 to k equals 550, so we're going to have 550 terms here and it's the sum from kĮquals 1 to k equals 550 of 2k plus 50, so whenever I try to evaluate a series, I like to just expand So assuming you've had a go at it, let's work through this together. See if you can figure out what this evaluates to. A finite series here expressed in sigma notationĪnd I encourage you to pause the video and
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