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A series is a special case of a sequence where the n'th term is the sum of n numbers a1, a2, ..., an. In other words, it is a sequence in the form S1 = a1 S2 = a1 + a2 S3 = a1 + a2 + a3 ... Sn = a1 + a2 + ... + an

Q: What is the difference between an infinite sequence and an infinite series?

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The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.

The next number is 25 but there are the sequence is infinite so there can be no end to the sequence.

The sum of the terms in a sequence is called a series. Sequence is a function whose domain is the natural numbers. So f(1)= first entry in the sequence, and f(2) is the next.... f(n) is the nth term. We usually don't write sequences that way. Instead of f(1) we write, a1 to refer to the first term. The function tells us the rule we use to find the terms of the sequence. So for example, f says take n and square it. Then the first 3 terms of the sequence are 1, 4 and 9 and the first 3 terms of the series are 1, 5 and 14

A geometric series.

An arithmetic series is the sequence of partial sums of an arithmetic sequence. That is, if A = {a, a+d, a+2d, ..., a+(n-1)d, ... } then the terms of the arithmetic series, S(n), are the sums of the first n terms and S(n) = n/2*[2a + (n-1)d]. Arithmetic series can never converge.A geometric series is the sequence of partial sums of a geometric sequence. That is, if G = {a, ar, ar^2, ..., ar^(n-1), ... } then the terms of the geometric series, T(n), are the sums of the first n terms and T(n) = a*(1 - r^n)/(1 - r). If |r| < 1 then T(n) tends to 1/(1 - r) as n tends to infinity.

Related questions

An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.

The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.

The next number is 25 but there are the sequence is infinite so there can be no end to the sequence.

The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.

There are an infinite series of numbers between 0.0001 and 0.001

Yes, with a difference of zero between terms. It is also a geometric series, with a ratio of 1 in each case.

what is the difference between N series and C series in nokia mobile phones

Each new number in the series is the sum of the previous two numbers. That sequence is part of an infinite series called the Fibonacci series.

difference between series is one pathway through circuit,difference between parralal is more then one pathway through circuit.

Succession of numbers of which one number is designated as the first, other as the second, another as the third and so on gives rise to what is called a sequence. Sequences have wide applications. In this lesson we shall discuss particular types of sequences called arithmetic sequence, geometric sequence and also find arithmetic mean (A.M), geometric mean (G.M) between two given numbers. We will also establish the relation between A.M and G.M

William John Swartz has written: 'On convergence of infinite series of images' -- subject(s): Infinite Series, Series, Infinite

An arithmetic series is a fairly similar to an arithmetic sequence except for the fact that in a series you are adding the numbers in between, not putting commas. Example: Sequence 1,3,5,7,.........n Series 1+3+5+7+..........+n Hope this helped(: