The function (sequence generator) f(x) with x∈ℕ has been defined as a recursive function (sequence), with the initial value defined for some x, ie starting form some some natural number (in this case 1), the value of the function (sequence) is given (in this case f(1) = 1), and each successive value of the function (sequence) is defined in terms of the current value f(x+1) = f{x} + g(x) where g(x) is a function with g(x) = 3x(x + 1).
f(x + 1) = f(x) + 3x(x + 1)
f(1) = 1
→ f(2) = f(1 + 1) = f(1) + (3×1)(1 + 1) = 1 + 3×2 = 1 + 6 = 7
→ f(3) = f(2 + 1) = f(2) + (3×2)(2 + 1) = 7 + 6×3 = 7 + 18 = 25
I'll let you evaluate the rest.
Hint:
f(4) = f(3 + 1) = f(3) + (3×3)(3 + 1)
f(5) = f(4 + 1) = f(4) + ...
f(6) = f(5 + 1) = f(5) + ...
No. The set of binary numbers includes fractions which are written in binary form. For example, binary(0.1) = decimal(0.5) which is not a natural number.
what are the seven properties of rational numbers
If at least one of the numbers is even, the result will be even. Otherwise all the numbers are odd and the result will be odd.
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
Let X be any set. A sequence in X is a function a: N -> X, where N is the natural numbers.
The Count function can be used if you are looking for just numbers and the Counta function if you are looking for numbers and text entries.
the atomic masses and atomic numbers... group number and period number... valence electrons and number of shells... these all determine the chemical properties of elements...
A sequence is a function ! whose domian is the set of natural numbers
Integers are a set of numbers including natural numbers (1, 2, 3...) their opposites (-1, -2, -3...) and 0.
properties of irrational numbers
No. The set of binary numbers includes fractions which are written in binary form. For example, binary(0.1) = decimal(0.5) which is not a natural number.
what are the seven properties of rational numbers
You do not need a function to determine the lowest common factor of two numbers. The lowest factor of any one number is 1. The lowest common factor of any two numbers is therefore 1 as well.
If at least one of the numbers is even, the result will be even. Otherwise all the numbers are odd and the result will be odd.
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
It is the set of natural numbers.
All natural numbers are rational numbers. No irrational numbers are natural numbers.