Question
16 32 Problem 1: For the geometric series 20 _ 8 + 5 25 Find the first term a and the ratio r_ Does the series converge or diverge (justify your answer)? If it converges, find its sum
16 32 Problem 1: For the geometric series 20 _ 8 + 5 25 Find the first term a and the ratio r_ Does the series converge or diverge (justify your answer)? If it converges, find its sum
Answers
$17-26$ Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
$$2+0.5+0.125+0.03125+\cdots$$
And this a question given the photo Wink Infant Geometric series. It's record to define whether the summation off this infinite cities called virgins to a certain element or diverges. So it says it's a geometric cities. Ah, first, fine, but the value of the common race you are and the coming race. You are just the second term over the first term or disturbed them over the second term, the fourth them over the certain s. So I'll just take any two, which is let's take one over 32 over one over 64. So it's the second term over the first time, and the value is two. So since since they told the Congress you are as equals to two, there is a rule for the I Could D geometric series, which say that if they come on race, you is less than warm. It converges if the greater than one, as in this case which are is listen is equals toe, too, and it's greater than one. Then it diverges. So the the Siri's diverges to infinity. So this is what diverges on. There's no specific limits, so it's just this is just the end of the question so just an easy way to determine whether the giant trick cities diverges for convergence by checking the value of the common ratio.
For that given geometric series. We can see that the first time a week or 10 in the commendation will be called departing the second time by the first time, which will be minus two. But then she called minus one by five. Now, since magnitude off honest, less than one. So we can say that there might be cities convert this So the 0.2 is converted Will make war, too, by one minus on what do you call to some off infinite terms. So that is it for 10 divided by one minus minus one by five. So this is a 4 to 25 by three.
Terminate this geometric serious could purchase or diverges. Go ahead and put this information for him Equals 0 to Infinity. Little girl for that. So We have here that R. is equal to 1/4, so many of our Just us, 2. 1. Therefore, it means that this series converges next part. We know what coverage is. We have Osama's Paying over. one was our is one. In this case we have 1/1 minus 1/4. She goes one over 3/4 that take the reciprocal and ankles for threats.
For the given geometric cities. The first term, aged 44 on the commendation, are for 23 by four. Things can be found out what they were doing the second time by the first time. Now, as you can see the magnitude of the common later, less than one. So the geometric series converges toe. Find the point where it converges. We need toe find as infectivity. Some off Donald Trump's that will be called by one minus are it took four, divided by one minus 35 is equal to four, divided by one minus what diverted One My Foot, which is 4 to 16.