Can an infinite series converge to a negative number?

Each of the partial sums of the series is positive. If the series converges then the lowest possible limit is 0. So the sums cannot add up to a negative number.

How does an infinite series converge?

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 the sum of an infinite series be a finite number?

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.

Are positive numbers infinite?

Originally Answered: How are numbers infinite? There is a very simple proof that the positive Integers (Natural Numbers) are infinite : Think of the biggest number you can think of – and call it N.

What is the sum of infinite positive numbers?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.

Is infinity positive or negative?

There is no such concept as negative infinity. Infinity can be related to anything that has constant recurrence, be it positive or negative. For Example. Take the number line.

How can the sum of all positive numbers be negative?

= -1. That is, the sum of positive numbers to infinity is negative. In the same way, it makes no sense to add up the positive numbers to infinity and say it equals -1/12.