Write the terms for each series and evaluate the sum, given that x1=-2, x2=-1, x3=0 x4=1, and x5

Write the terms for each series and evaluate the sum, given...

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a list of numbers with a constant difference between consecutive terms. This concept is useful for identifying and writing the terms of the series when given the first term and the common difference, allowing one to determine any term in the sequence using a formula.

Series Summation

Series summation involves adding together the terms of a sequence. In mathematics, this process is foundational for understanding how individual terms contribute to an overall sum. Mastery of summing series includes both writing out the individual terms and using formulas or properties of arithmetic progressions to efficiently compute the total.

Transcript

00:01 All right, in this video, we're looking at evaluating a sum using the sigma notation.

00:06 So in this problem here, we have the sigma symbol, which again means sum of.

00:10 The lower end of the sigma, we have i equal to one.

00:13 That's basically the starting point to our sigma, and the top part of our sigma have a four.

00:17 That's our ending number.

00:19 We also need a, before we find the sum, write out what terms are in the series, and of course, we all can have to find the sum.

00:26 All right.

00:26 So the first thing to do is start plugging in my different values for i, so i can get those terms for the series, and then, of course, i'm going to add them all up.

00:34 Okay, so to find the first term of the series are a subscript 1, we're plugging in 1 for i to start off with, because that's where my stigma starts.

00:42 So this is where my stigma starts.

00:44 This is where it ends.

00:47 All right here, we're placing that with a 1.

00:50 So i have x, subscript 1 to the 3rd, plus 1 ,000 over x, subscript 1 plus 10.

00:58 Now, in the directions to the problem, they told you already what x, subscript whatever number is equal to already.

01:05 In this case, x -subscript 1 is negative 2.

01:08 So x -subscript 1 is negative 2.

01:11 X -substcript 2 is negative 1.

01:15 X -substrip 3 is 0.

01:17 Again, these are in the directions of the problem.

01:20 Make that a little better.

01:23 Okay, and x -subscript 4 is 1.

01:26 They did give you x -subscript 5, but in this question because we're only going up to 4, i don't need to write that one down.

01:30 All right, so where i have x, subscript one, i'll replace that with a negative two, and then i'm just working out that math in my calculation.

01:42 So you just can use a calculator to kind of compute this number out.

01:45 You'll eventually get to a fraction, which can be reduced, and you'll get 124.

01:49 Okay, so that's the first term of the series.

01:51 Okay, to get to the second term, i'm just going in order.

01:53 So i got one, and then x would be two.

01:55 So i got x subscript two to the third...

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