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Emilijo
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Does exist general formula for nth term in sequence if I have generative function?
In my case, generative function is (1/(1-x))-(1/(1-x^3)).
In my case, generative function is (1/(1-x))-(1/(1-x^3)).
I think so but you may have to give the 1st 3 terms and the generating function.Emilijo said:Does exist general formula for nth term in sequence if I have generative function?
In my case, generative function is (1/(1-x))-(1/(1-x^3)).
Emilijo said:I don't have to give 1st 3 terms. If I have generating function, the sequence is strictly given, and I just want to have formula for getting nth term in the sequence.
Now, what is the formula?(general formula, and formula for my case)
Emilijo said:If I have generating function, the sequence is strictly given
A generating function is a mathematical function that encodes information about a sequence of numbers. It can be used to find the values of the terms in the sequence or to manipulate the sequence in various ways.
To find the formula for the nth term using a generating function, you first need to express the sequence as a power series. Then, you can use algebraic manipulations and the properties of power series to find the formula for the nth term.
The properties of a generating function include linearity, shifting, and scaling. Linearity means that the generating function of a sum of sequences is equal to the sum of the individual generating functions. Shifting means that the generating function of a shifted sequence is equal to the original generating function multiplied by a power of x. Scaling means that the generating function of a scaled sequence is equal to the original generating function raised to a power.
Yes, a generating function can be used to find any term in a sequence as long as the sequence can be expressed as a power series and the generating function is known. However, depending on the complexity of the sequence and the generating function, it may be difficult or impossible to find the formula for the nth term.
A generating function is different from a regular function in that it encodes information about a sequence, while a regular function operates on individual values. A regular function has a specific input and output, while a generating function can have multiple inputs and outputs. Additionally, generating functions often involve power series and other mathematical concepts that are not typically used in regular functions.