The two expressions are :-
1. ((n+1)^3/((n+2)^3)) + ((n-1)^3/(n^3)) is approximately 2 - (6/(n+2) + 2/((n+2)^2))
2. (n^3/((n+1)^3)) + ((n-1)^3/(n^3)) is approximately 2 - (6/(n+1) - 3/((n+1)^2))
1. ((n+1)^3/((n+2)^3)) + ((n-1)^3/(n^3)) is approximately 2 - (6/(n+2) + 2/((n+2)^2))
2. (n^3/((n+1)^3)) + ((n-1)^3/(n^3)) is approximately 2 - (6/(n+1) - 3/((n+1)^2))
I can possibly continue to give approximate expressions of these types.
ReplyDeleteActually my paper on 'Rational Number Series' was good.
You get triangle series.
You get prime numbers.
You get infinite series of geometric progression.
You get finite series till certain number of terms of geometric progression.
The above are finite series till certain number of terms of geometric progression.
I can give more and more such expressions. But stopping with this. Hope you have understood the concept.