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It is possible for an infinite series to have a finite sum if it is of a "special" kind. Consider the infinite series of fractions that is 1/2, 1/4, 1/8, 1/16,...1/n. You can see that each term is 1 over twice the denominator of the previous term. (We might have written the last term as 1/2n where n is the number of the term.) In this series there are an infinite number of elements, but the sum will be 1. In the case of the series, 1/2 + 1/4 + 1/8 + 1/16 +... + 1/n, the sum has a limit of 1, and 1 will be the sum of the terms at infinity. Let's do the math. Add the first two terms, get a sum, than add the next term to get another sum, then add the next term to get another sum, and on, and on: 1/2 + 1/4 = 3/4, then 3/4 + 1/8 = 7/8, then 7/8 + 1/16 = 15/16, then 15/16 + 1/32 = 31/32. By simple inspection, you can see that the sum is increasing, but is "creeping up" by smaller and smaller increments. You can see where the series is going. It will go to infinity, but each term is getting smaller and smaller. Thinking about it, the terms will approach zero as they get infinitely large. And each term will bring the series closer to summing to 1. At infinity, the sum will be 1.
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What is the sum of an infinite geometric series is?
It depends on the series.
What is the sum of infinite numbers?
The sum of the infinite is infinite or a finite number, depending on the numbers that you are summing up.Sometimes an infinite series will converge to a finite answer. An example of one that results in an infinite answer should be fairly easy. Consider 1+2+3+4+5+6+.... Each number is bigger than the previous.But what about when each term is smaller than the previous. Consider this example, which most people should be familiar with. Take the decimal equivalent for 1/3, which is 0.3333333.... We know this is a finite number. This can be written as an infinite series 3/10 + 3/100 + 3/1000 + . . . . + 3/(10n). We would say that this infinite series converges to 1/3.Look at this one: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + .... Each term is 1/2 the previous term. As the terms are added, the sum of the series would look like this: 1/2, 3/4, 7/8, 15/16, 31/32,... Notice that each sum is half way between the previous sum and 1, but will never get to 1. This series converges to 1.Not every series, where the terms decrease, will converge to a finite number though. I won't show how, here, but the series 1/2 + 1/3 + 1/4 + 1/5 + . . . + 1/n, does not converge but goes to infinity. Each term is smaller than the previous, but they are not getting small 'fast enough' to converge to a finite number.
What is the sum of the infinite geometric series?
The sum of the series a + ar + ar2 + ... is a/(1 - r) for |r| < 1
Is null set finite or infinite?
finite
What the differentiate between finite set and infinite set?
A finite set has a finite number of elements, an infinite set has infinitely many.
