What is the sum of the infinite geometric sequence 24 12 6 3?

What is the sum of the infinite geometric sequence 24 12 6 3?

16
The sum of the geometric series 24 – 12 + 6 – 3 + . . . is 16.

How do you find the infinite sum of a geometric series?

To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r , where a1 is the first term and r is the common ratio.

What is the sum of the geometric sequence 24 if there are 7 terms?

-159964
The sum of the geometric sequence -4, 24, -144.if there are 7 terms is S7 = -159964.

What is the limit of an infinite sum?

The value of this limit is called the limiting sum of the infinite geometric series. The values of the partial sums Sn of the series get as close as we like to the limiting sum, provided n is large enough. S∞=limn→∞Sn=a1−r.

What is the sum of the series?

The sum of the terms of a sequence is called a series . If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn , without actually adding all of the terms.

What equation is equal to infinity?

In short, any real number x, when added to infinity gives infinity again. That is, x + infinity = infinity (where x is a real number). A simple answer: infinity – infinity is zero!

What is the sum of infinite series?

The sum of infinite terms that follow a rule. When we have an infinite sequence of values: 1 2 , 1 4 , 1 8 , 1 16 , which follow a rule (in this case each term is half the previous one), and we add them all up: 1 2 + 1 4 + 1 8 + 1 16 + = S. we get an infinite series.

Can the infinite sum be taken to be equal to 1/2?

Since it follows that which is nonsense. So the assertion that the infinite sum can be taken to equal to 1/2 is not correct. In fact, you can derive all sorts of results messing around with infinite sums that diverge (see here ). It’s a trick!

What is the sum of all integers between 1 and 4?

Other notations for summation include [1, 2, 3, 4] for the sum of all integers between 1 and 4, as well as shorthand notations such as 1, 2, 99, 100 referring to the sum of all integers from 1 to 100. 1^n, 2^n, 10^n could be used to denote a series of numbers raised to the power of n.

What is the sum of -1+2+3+4+?

1+2+3+4+… then the answer to this sum is -1/12. The idea featured in a Numberphile video (see below ), which claims to prove the result and also says that it’s used all over the place in physics. People found the idea so astounding that it even made it into the New York Times. So what does this all mean?