How can the sum of an infinite series converge to a finite number?

An infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute value of the summand is finite. More precisely, a real or complex series ∑∞n=0an ∑ n = 0 ∞ a n is said to converge absolutely if ∑∞n=0|an|=L ∑ n = 0 ∞ | a n | = L for some real number L .

Can infinite series have finite sum?

Convergent series An easy way that an infinite series can converge is if all the an are zero for n sufficiently large. Such a series can be identified with a finite sum, so it is only infinite in a trivial sense.

Who was able to show that one can get a finite value by adding infinite terms or a finite value can be expressed as an infinite series?

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How do you find the sum of a finite series?

To find the sum of a finite geometric series, use the formula, Sn=a1(1−rn)1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio .

What is the value of an infinite sum?

An infinite series has an infinite number of terms. The sum of the first n terms, Sn, is called a partial sum. If Sn tends to a limit as n tends to infinity, the limit is called the sum to infinity of the series. The sum of infinite arithmetic series is either +∞ or – ∞.

How do you add infinite series?

In finding the sum of the given infinite geometric series If r<1 is then sum is given as Sum = a/(1-r). In this infinite series formula, a = first term of the series and r = common ratio between two consecutive terms and −1

How can an infinite series have a finite sum?

An infinite series can have a finite sum because the terms you add get smaller and smaller, and you’re adding an infinity of them. Obviously not all the series are convergent (meaning, their sum is a finite number), and that’s the case when the terms don’t get smaller (imagine 1 + 2 + 3 + 4 + 5 + …,…

Why is an infinite ordered sequence equal to a finite number?

You are obviously confusing the infinite series (which is an object that could be represented by an infinite ordered sequence of numbers), and the SUM of the infinite series which is just a number. So of course, it might seem strange that an infinite sequence is equal to a finite number. That’s because it doesn’t make sense.

What is the value of Infiniti infinite?

Infinite is infinite, it can be always a bigger value, no matter what we write to $n$. For an incredibly big calue, the sum must be bigger. I mean, we can prove that for a given $n$, the sum becomes bigger than 1.7, or 1.8, kor 1.95, et cetera.