Here is the remainder class with remainder 1: We say that these are the numbers congruent to 0 modulo 3. Here is the remainder class with remainder 0:Īlgebraically, these are the number 3 k. Upon division of a number by 3, for example, the remainder will be either 0, 1, or 2. In the Appendix to Arithmetic, we saw that the sum of consecutive numbers - a triangular number - is given by this formula: Then the sum is equal to the number of terms times that constant. If the argument of the summation is a constant, that is, does not depend on the index k, Use sigma notation to indicate these sums. As for the upper index, we can decide that it must be 50 because we must have 2 k = 100. To ensure that 2 is the first term, the lower index is clearly 1. Use sigma notation to indicate this sum:Ģ k indicates an even number, which is a multiple of 2. See Lesson 13 of Algebra, Example 1 and Problem 7.Įxample 3. But when k is odd, (−1) k will be negative. For when k is 0 or an even number, then (−1) k will be +1. What causes the signs to alternate is (−1) k. When the signs alternate, positive and negative in that way, we call that an alternating series. That is how with sigma notation we indicate a polynomial in x of degree n.
We indicate the next to last as ( n − 1).
SIGMA MATH HOW TO
That is how to use sigma notation to indicate the sum of n consecutive whole numbers. To cover the answer again, click "Refresh" ("Reload"). To see the answer, pass your mouse over the colored area. K is called a dummy index because it does not actually affect the sum, and we could indicate that sum using any letter we please for example j: In other words, we are to repeatedly add ka k, which we call the argument of the sum, or the summand, starting with k = 1 and ending with k = 4.
The next time, we put k = 2, then 3, and so on, until we come to the upper index, which in this case is 4. That is indicated by the lower index of Σ. The first time we write it, we put k = 1. This means that we are to repeatedly add ka k.
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