New Binomial Expression

I have worked on Rational number series or what I have termed as consecutive number theory a lot for the last three years.

I have come up with a myriad of expressions simply by tweaking around with the individual terms in the expressions. 

I have continued it further today.

I have made a binomial expression. Here it is

Also

Feel free to check this expression and do let me know if there is an error.

Hope you have a nice day !!