Find the sum of each infinite geometric series. 2 - 1 + 1/2 - 1/4...

Question

Find the sum of each infinite geometric series. 2 - 1 + 1/2 - 1/4 + ...

Accepted Answer

Welcome back. I'm so glad you're here. We have been given an infinite geometric series and we need to find the sum. Well, first of all we have to see if we can do that because the ratio has to meet certain criteria to be able to find a sum of an infinite geometric series. So what is that criteria? Well Our has to be between -1 and one. So let's find out if it is. We know it's a geometric series. So let's find the ratio. We find the ratio by taking any two terms right next to each other to subsequent terms. And we're going to take the second one that we choose divided by the one immediately proceeding it. I'll just take the second term a sub two and divided by the one immediate immediately preceding it. A sub one. A sub two is negative three And a sub one is 9 That simplifies to negative 1/ is negative one third in between negative one and one. Yes it is. We may proceed. So we recall from previous lessons that the formula for the sum of an infinite geometric series. Meeting that criteria for the R value is a sub one divided by one minus R. And we already know a lot of this. A sub one that's the value of the first term. We already got that one that's nine and we know one is one minus R. R. Well R is negative one third. So we can just simplify. We've got nine divided by Okay, one minus negative one third is one plus one third which is four thirds. We can rewrite this as nine divided by four thirds like this because that can remind us that we just need to multiply by the reciprocal of the second term or nine times 3/4 And then we can just multiply straight across. That's 27/4 and simplifying that because our number our answers are with a decimal, that is going to be 6.75. We look at our answer choices and that matches with answer choice d. While done, we'll catch you on the next one.

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Find the sum of each infinite geometric series. 2 - 1 + 1/2 - 1/4 + ...