Common formulas of split term elimination method 1/n(n+1)(n+2)=?

Common formulas of split term elimination method 1/n(n+1)(n+2)=?

Original formula = 1 / [n (n + 1)] - 1 / [n (n + 2)]
=1/n-1/(n+1)-[1/2n-1/2(n+2)]
=1/2n-1/(n+1)+1/2(n+2)

Solving problems with the method of split term elimination
How to eliminate the split terms in BN = 3 / {(6n-5) (6N + 1)}

I guess this formula is just a part of your comprehensive problem^^
The BN you gave can only be split terms. After splitting terms, it can't be cancelled because there are only two terms. Many terms are needed to simplify the split terms cancellation
The formula of split term can be written as follows:
a/[(n)(n+b)]=a/b[1/n-1/(n+b)]
So, when it comes to your topic,
Bn=3/[(6n-5)(6n+1)]=3/（6n+1-6n+5）[1/（6n-5）-1/（6n+1）]
=1/2[1/（6n-5）-1/（6n+1）]
If this problem is not clear, you can baidu Hi me yo!

Some problems about the split term elimination method
This formula is from the book: 1 / N (n + k) = 1 / k * (1 / n-1 / N + k)
Why does it sometimes split and become 1 / K, sometimes K or something else?

The essence of the split term method is to decompose each term (general term) in the sequence, and then recombine them, so that some terms can be eliminated, and finally the purpose of summation can be achieved. The general term decomposition (split term) is as follows: (1) 1 / N (n + 1) = 1 / n-1 / (n + 1)