What is the difference between squences and series in the topic of sequece and summation of series?
Please try to explain and any examples would be appreciated!
2006-12-20 05:00:30 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
o great i just misasked a question
2006-12-20 05:03:44 · update #1
A sequence is a number pattern in a definite order following a certain rule
A series is a sum of terms in a sequence.
2006-12-20 05:05:27 · answer #1 · answered by raj 7 · 0⤊ 0⤋
In mathematics, a series is often represented as the sum of a sequence of terms. That is, a series is represented as a list of numbers with addition operations between them, for example this arithmetic sequence:
1 + 2 + 3 + 4 + 5 + ... + 99 + 100
In most cases of interest the terms of the sequence are produced according to a certain rule, such as by a formula, by an algorithm, by a sequence of measurements, or even by a random number generator.
Series may be finite, or infinite; in the first case they may be handled with elementary algebra, but infinite series require tools from mathematical analysis if they are to be applied in anything more than a tentative way
2006-12-20 05:29:30 · answer #2 · answered by yason 2 · 0⤊ 0⤋
Sequences are basically just a listing of numbers. They are LIKE sets but aren't, in that numbers can repeat themselves. The following are sequences:
1, 3, 5, 7, 9, ......,
1, -2, 4, -8, 16, -32, .....,
Series, on the other hand, are summations. The following are series:
1 + 2 + 3 + 4 + 5 + ..... + n
Series are usually written in sigma notation. I can't make the symbol here, but you would usually have:
SIGMA (i = 1 to n, i).
The i would be written under the sigma symbol, the n on top of the sigma symbol, and you would iteratively go through the values of 1 to n replacing i and then adding.
2006-12-20 05:07:03 · answer #3 · answered by Puggy 7 · 0⤊ 0⤋
Yes, as indicated in other posts..... sequence is a list of numbers (or whatever) while series is the sum of those things. One subtlety is that with series (sums) you have the concept of partial sums (adding up only finitely many terms), and the partial sums form a sequence.
So for instance, there is the (geometric) sequence: 1,1/2,1/4, 1/8,1/16,1/32 ....1/2^n.... Then there is the series 1+1/2+ ...+ 1/2^n+... Then there are the partial sums for this series, which are 1,3/2, 7/4, 15/16, .... etc. These partial sums converge to the number 2. That is why we say the series converges to the number two: because the sequence of partial sums converges.
Hope this helps.
2006-12-20 05:11:27 · answer #4 · answered by a_math_guy 5 · 0⤊ 1⤋
Summation are like a series of events. Like Zeno's Arrow. If u half each distance between the tip and the target infinitely I'm sure the arrow will never arrive.I'm sure that the sequence of events will end in time.Motion and d are involved in that example.It's all math and some philosophy
2006-12-20 05:07:15 · answer #5 · answered by ? 5 · 0⤊ 0⤋
A series is a sum of a sequence.
1,3,5,7,9... is a sequence.
1+3+5+7+9... is a series.
2006-12-20 05:03:06 · answer #6 · answered by x 4 · 0⤊ 0⤋