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The principle of split term elimination I don't know how
This is the concrete application of the idea of decomposition and combination in the summation of sequence. The essence of 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
（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)!-n!
Help me to calculate the process of 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + 1 / 32 with the split term elimination method
Original formula = 1-1 / 2 + 1 / 2-1 / 4 + 1 / 4-1 / 8 + 1 / 8-1 / 16 + 1 / 16-1 / 32 = 31 / 32
Primary school split term elimination method
1 / 2 * (1 + 1 / 2-1 / 2008-1 / 2009) answer
1/4018
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