For senior high school mathematics sequence with reverse order addition, split term method, combination method sum example RT!

For senior high school mathematics sequence with reverse order addition, split term method, combination method sum example RT!

1. Addition of flashback:
The most basic
1+2+3+4…… +100
=(1+100)+(2+99)+(3+98)...(48+53)+(49+52)+(50+51)
=101*50
=5050
It's a little more complicated
F {x} = 1 / [2 ^ x + √ 2] find f [- 5] + F {- 4} + +f{0}+…… +The value of F {5} + F {6}
So s = f (- 5) + F (- 4) + +f(0)+…… +f(5)+f(6)
S=[f(-5)+f(6)]+[f(-4)+f(5)]+[f(-3)+f(4)]+[f(-2)+f(3)]+[f(-1)+f(2)]+[f(0)+f(1)]
And f (- 5) + F (6)... F (0) + F (1) all satisfy the form of F (x) + F (1-x)
Even if the value of F (- 5) + F (6)... F (0) + F (1) is √ 2 / 2
So s = 6 ×√ 2 / 2 = 3 √ 2
2. Split term method
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!
ordinary
1. Find the sum of the first n terms of the sequence an = 1 / N (n + 1)
Let an = 1 / N (n + 1) = 1 / n-1 / (n + 1) (split term)
Then Sn = 1-1 / 2 + 1 / 2-1 / 3 + 1 / 4 +1 / n-1 / (n + 1) (sum of split terms)
　　＝ 1-1/(n+1)
　　＝ n/(n+1)
complex
3. Merger method