Split term method, which is the concrete application of the idea of decomposition and combination in the summation of series. It is to decompose each item (general item) in the sequence, and then recombine it, so that it can eliminate some items and finally achieve the purpose of summation. The relationship between multiples of general term decomposition (split term).
1, split term expression:1/[n (n+1)] = (1/n)-[1/(n+1)].
2. The summation formula of split term method is as follows:
( 1) 1/[n(n+ 1)]=( 1/n)-[ 1/(n+ 1)].
(2) 1/[(2n- 1)(2n+ 1)]= 1/2[ 1/(2n- 1)- 1/(2n+ 1)].
(3) 1/[n(n+ 1)(n+2)]= 1/2 { 1/[n(n+ 1)]- 1/[(n+ 1)(n+2)]} .
(4) 1/(/a+/b)=[ 1/(a-b)](/a-/b).
(5)n n！ =(n+ 1)！ -No! .
(6) 1/[n(n+k)]= 1/k[ 1/n- 1/(n+k)].
(7) 1/[/n+√( n+ 1)]= √( n+ 1)-n .
(8) 1/(/n+/n+k)=( 1/k)[(n+k)-/n].
Definition of crack elimination method
The elimination of the split term of a series is to split the general term into the form of "the difference between two terms", so that most items can be "offset" when summing, leaving a few items.
Three characteristics:
1, the molecules are all the same, the simplest form is 1, and the complex form can all be x(x is any natural number), but as long as X is extracted, it can be converted into the operation that the molecules are all 1.
2. The denominator is the product of several natural numbers, and the factors on two adjacent denominators are "end to end".
3. The difference of several factors on the denominator is a constant value. The core link of differential operation is "to achieve the purpose of simplification through two-phase elimination"