Highly Multiplicative Series

In the Fibonacci series we have two numbers by adding them we get a series consisting of even and odd numbers in this it goes up to infinity we can track any n th number by the Binet’s formula. I have just thought of the multiplication of the first two terms and continued till where I can go, it means that the first two terms in the form (a, b) we will continue the multiplication as we do the addition in the Fibonacci series. As a result we will get the big integers from the 7th term approximately which is obvious by multiplying to its previous one it will come to an a very big integer which cannot be accountable by some range. If we do the multiplication the first two terms will be the same however from the third term it can be written as the power of that integers in which the powers will be following the Fibonacci series in this we can also find the n th term for the multiplicative series. Here the first two terms will in the same order as it will be given to find the series by changing the order it will violates the rule of restricted term. The meaning of the restricted here is that the order of (a, b) will be the same throughout the calculation of whole series we cannot alter that if we do so them it will not be more restricted term. So there are two concept in the multiplicative series restricted and non-restricted series. If the (a, b) is there and the operation is going on then it can be said as the restricted series if it is given (a, b) and asked for the (b, a) series then it is said as non-restricted series. I have considered 4 possible criteria to check the pairing of the variables (a, b). We will get to know about the series and also the n th term value of that series for all possible solutions.

Recommended citation: Vishal Pandey . HIGHLY MULTIPLICATIVE SERIES. TechRxiv. February 22, 2022. DOI: 10.36227/techrxiv.19126634.v1
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