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The natural numbers 0 and 1 are trivial sum-product numbers for all , and all other sum-product numbers are nontrivial sum-product numbers. For example, the number 144 in base 10 is a sum-product number, because 1 + 4 + 4 = 9 {\displaystyle 1+4+4=9} , 1 × 4 × 4 = 16 {\displaystyle 1\times 4\times 4=16} , and 9 × 16 = 144 {\displaystyle 9 ...
Use of a user-defined function sq(x) in Microsoft Excel. The named variables x & y are identified in the Name Manager. The function sq is introduced using the Visual Basic editor supplied with Excel. Subroutine in Excel calculates the square of named column variable x read from the spreadsheet, and writes it into the named column variable y.
The formula for calculating the average is based on the manipulation of the cells, in the form =C2/B2. As the spreadsheet is unaware of the user's desire for D to be an output column, the user copies that formula into all of the cells in D. However, as the formula refers to data on different rows, it must be modified as it is copied into the ...
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
Row labels are used to apply a filter to one or more rows that have to be shown in the pivot table. For instance, if the "Salesperson" field is dragged on this area then the other output table constructed will have values from the column "Salesperson", i.e., one will have a number of rows equal to the number of "Sales Person". There will also ...
We prove associativity by first fixing natural numbers a and b and applying induction on the natural number c. For the base case c = 0, (a + b) + 0 = a + b = a + (b + 0) Each equation follows by definition [A1]; the first with a + b, the second with b. Now, for the induction. We assume the induction hypothesis, namely we assume that for some ...
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
The next number in the sequence (the smallest number of additive persistence 5) is 2 × 10 2×(10 22 − 1)/9 − 1 (that is, 1 followed by 2 222 222 222 222 222 222 222 nines). For any fixed base, the sum of the digits of a number is proportional to its logarithm ; therefore, the additive persistence is proportional to the iterated logarithm .