In Exercises 37–44, find the sum of each infinite geometric serie...

Question

In Exercises 37–44, find the sum of each infinite geometric series.1 + 1/3 + 1/9 + 1/27 + ...

Accepted Answer

Hey everyone in this problem we are given an infinite series and were asked to evaluate this cell. Okay. This series we're given is one plus 1/4 plus 1/16 plus 1/64 plus dot dot dot. Okay, so let's recall the general format. We're dealing with arithmetic, some like this. Okay, so we have the sum from zero to infinity. This is an infinite series. We're going all the way to infinity of A. R times I. Okay. And our is going to be our common ratio. Okay. So what do we multiply the previous term by to get the new term? K and A is going to be that initial. Alright, so A in this case that initial term is going to be one. Okay. What about our we need to find our and again r is a common ratio. What do you have to multiply the term we're at to get to the next term. Okay, so we can find that by dividing one term by its previous term. Okay, so we can take one quarter, divide by one. Can we get one quarter? We can do the same for the next term. So the next term is 1/16. We divided by the previous term. 1/4. Okay. And again we get 1/4. We can do it once more if you want. We can do one over 64. Okay. And it's always a good idea to check all of the terms just to make sure that we're looking at the right type of sequence? Our series. Okay. 1/64 divided by 1/16. And again this gives us 1/4. Okay, so we have our is 1/4. We have a as one and so we can write our some as I equals zero to infinity of a. One times. Are 1/4 to the exponent I. Okay. Alright, great. Now what? We're given a sum like this, you see that this is geometric, Okay, or the inside geometric sequence. We're doing some of this and so the infinite some Can be given as a over 1 -2. Okay, we know our A we know our our let's plug those in and we're going to get 1/1 minus a quarter which is gonna be one divided by three quarters, Which is going to be 4/3. Okay. And so the some Of this infinite series that we're given is 4/3. That's going to be answer. B Thanks everyone for watching. I hope this video helped see you in the next one.

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In Exercises 37–44, find the sum of each infinite geometric series.1 + 1/3 + 1/9 + 1/27 + ...

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