• Kirtivasan Ganesan

Maclaurin series and series of Euler number are basic series and are taught all over the world to children. The series based on Maclaurin and Euler number are fundamental in nature. But an important development to the Maclaurin series and Euler number is the use of consecutive numbers. Consecutive numbers are not just a mindset of all of us. They help in the development of functions similar to Maclaurin series and Euler number. 4.666 is the number that we get when consecutive numbers are used following the Maclaurin series and the Euler Number e series. In this paper the basic Maclaurin series and e series are outlined and also rigorous explanation and the similarity to the consecutive number based 4.666 series are explained.

Maclaurin series, Euler number e, e series, 4.666 series, sin(x) series, cos(x) series, one(x) series, zero(x) series

"4.666 based expressions", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 9, page no.e224-e233, September-2025, Available :http://www.jetir.org/papers/JETIR2509424.pdf

"4.666 based expressions", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 9, page no. ppe224-e233, September-2025, Available at : http://www.jetir.org/papers/JETIR2509424.pdf