Wikipedia
sigma notation : Summation is the addition of a set of numbers; the result is their sum or total. An interim or present total of a summation process is termed the running total. The "numbers" to be summed may be natural numbers, complex numbers, matrices, or still more complicated objects. An infinite sum is a subtle procedure known as a series. Note that the term summation has a special meaning in the context of divergent series related to extrapolation. The summation of 1, 2, and 4 is 1 + 2 + 4 = 7. The sum is 7. Since addition is associative, it does not matter whether we interpret "1 + 2 + 4" as (1 + 2) + 4 or as 1 + (2 + 4); the result is the same, so parentheses are usually omitted in a sum. Finite addition is also commutative, so the order in which the numbers are written does not affect its sum. (For issues with infinite summation, see absolute convergence.) If a sum has too many terms to be written out individually, the sum may be written with an ellipsis to mark out the.. More from Wikipedia
sigma notation : In mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and associated names for this idea: Mandel notation, Mandel-Voigt notation and Nye notation are others found. Kelvin notation.. More from Wikipedia
Sigma Notation
Sigma Notation - The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..
Sigma Notation - The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..Sigma Notation
The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3..
Sigma Notation - Introduction Sum of Sequence Visit sKoolplusplus.com for the clear video.
Please visit us at www.isallaboutmath.comSigma Notation. Tetrahedral numbers. Pyramidal Numbers. Some relations between them.
Question : I do not understand how to use sigma notation in writing a series. Is there a process to figuring it out (such as using the arithmetic sequence formula to find the nth term/limits) or is it by inspection (finding a general pattern/guess and check)?
Answer : Hi - how you determine the sigma notation for a series depends on what information you're given, but it's almost always a shorthand for the sum of a large series of numbers: The number above the sigma is the upper bound of the summation (or the last variable value in the series), and the equality on the bottom (something like x=1 is the lower bound, or the first variable value in the series). It's usually not a trial-and-error formula - you should be able to use the given information to set up a summation (sigma) formula. But you're right that arithmetic sequences sometimes play arole in sigma notation - indeed the material to the right of the sigma (the expression contains the variable whose bounds are given above and below the sigma) is an arithmetic sequence that can be used to find the value in the series for a given value of the variable (what you rightly call the "nth term"). Limits can also be used (usually on top) - to say "as x approaches 0" or "as x approaches infini.... More from Yahoo Answers
Answer : Hi - how you determine the sigma notation for a series depends on what information you're given, but it's almost always a shorthand for the sum of a large series of numbers: The number above the sigma is the upper bound of the summation (or the last variable value in the series), and the equality on the bottom (something like x=1 is the lower bound, or the first variable value in the series). It's usually not a trial-and-error formula - you should be able to use the given information to set up a summation (sigma) formula. But you're right that arithmetic sequences sometimes play arole in sigma notation - indeed the material to the right of the sigma (the expression contains the variable whose bounds are given above and below the sigma) is an arithmetic sequence that can be used to find the value in the series for a given value of the variable (what you rightly call the "nth term"). Limits can also be used (usually on top) - to say "as x approaches 0" or "as x approaches infini.... More from Yahoo Answers
Question : How do I use sigma notation in order to express the upper sum and the lower sum of f(x) = (x^2/9) +1 obtained by dividing the interval [0,3] into n equal intervals?
I do not get this problem at all, especially with the part when it states I have to divide the interval into "n equal intervals."
Thanks for your help!
Answer : You divide the interval into n equal subintervals, on each subinterval you approximate the height of a rectangle which which is "about" the height of the function, you multiply by the length of the subinterval, and you have found the area of the rectangle which is approximating the area under the curve on the subinterval. Then you add up these approximations and take the limit as n becomes infinite; by definition, the result is the definite integral of f(x) over [0,3]. When [0,3] is partitioned into n subintervals of equal length, the subintervals are [0,3/n], [3/n,6/n], ..., [3*(n-1)/n,3*n/n]. Since the function x^2/9 + 1 is increasing over the interval [0,3], the lower sum will be found using the evaluations of the function at the left end of the subinterval, and the upper will use the right end. We will show the work for the upper sum. The function at the right end of the n-th subinterval is (3k/n)^2/9 + 1, and the length of the subinterval is 3/n, so we will have the produ.... More from Yahoo Answers
Answer : You divide the interval into n equal subintervals, on each subinterval you approximate the height of a rectangle which which is "about" the height of the function, you multiply by the length of the subinterval, and you have found the area of the rectangle which is approximating the area under the curve on the subinterval. Then you add up these approximations and take the limit as n becomes infinite; by definition, the result is the definite integral of f(x) over [0,3]. When [0,3] is partitioned into n subintervals of equal length, the subintervals are [0,3/n], [3/n,6/n], ..., [3*(n-1)/n,3*n/n]. Since the function x^2/9 + 1 is increasing over the interval [0,3], the lower sum will be found using the evaluations of the function at the left end of the subinterval, and the upper will use the right end. We will show the work for the upper sum. The function at the right end of the n-th subinterval is (3k/n)^2/9 + 1, and the length of the subinterval is 3/n, so we will have the produ.... More from Yahoo Answers
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