关于一般数列的求和有哪几种典型的题目?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/30 22:15:42
关于一般数列的求和有哪几种典型的题目?
尽量全面一些,
尽量全面一些,
![关于一般数列的求和有哪几种典型的题目?](/uploads/image/z/20304641-65-1.jpg?t=%E5%85%B3%E4%BA%8E%E4%B8%80%E8%88%AC%E6%95%B0%E5%88%97%E7%9A%84%E6%B1%82%E5%92%8C%E6%9C%89%E5%93%AA%E5%87%A0%E7%A7%8D%E5%85%B8%E5%9E%8B%E7%9A%84%E9%A2%98%E7%9B%AE%3F)
1+2+3+.+n=n(n+1)/2
2.1^2+2^2+3^2+.+n^2=n(n+1)(2n+1)/6
3.1^3+2^3+3^3+.+n^3=( 1+2+3+.+n)^2=n^2*(n+1)^2/4
4.1*2+2*3+3*4+.+n(n+1)=n(n+1)(n+2)/3
5.1*2*3+2*3*4+3*4*5+.+n(n+1)(n+2)=n(n+1)(n+2)(n+3)/4
6.1+3+6+10+15+.
=1+(1+2)+(1+2+3)+(1+2+3+4)+.+(1+2+3+...+n)
=[1*2+2*3+3*4+.+n(n+1)]/2
=n(n+1)(n+2)/6
7.1+2+4+7+11+.+ n
=1+(1+1)+(1+1+2)+(1+1+2+3)+.+(1+1+2+3+...+n)
=(n+1)*1+[1*2+2*3+3*4+.+n(n+1)]/2
=(n+1)+n(n+1)(n+2)/6
8.1/2+1/2*3+1/3*4+.+1/n(n+1)
=1-1/(n+1)=n/(n+1)
9.1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+...+n)
= 2/2*3+2/3*4+2/4*5+.+2/n(n+1)=(n-1)/(n+1)
10.1/1*2+2/2*3+3/2*3*4+.+(n-1)/2*3*4*...*n
=(2*3*4*...*n-1)/2*3*4*...*n
11.1^2+3^2+5^2+.(2n-1)^2=n(4n^2-1)/3
12.1^3+3^3+5^3+.(2n-1)^3=n^2(2n^2-1)
13.1^4+2^4+3^4+.+n^4=n(n+1)(2n+1)(3n^2+3n-1)/30
14.1^5+2^5+3^5+.+n^5=n^2 (n+1)^2 (2n^2+2n-1) /12
15.1+2+2^2+2^3+.+2^n=2^(n+1) – 1
不在其中的发给我.我给你算
2.1^2+2^2+3^2+.+n^2=n(n+1)(2n+1)/6
3.1^3+2^3+3^3+.+n^3=( 1+2+3+.+n)^2=n^2*(n+1)^2/4
4.1*2+2*3+3*4+.+n(n+1)=n(n+1)(n+2)/3
5.1*2*3+2*3*4+3*4*5+.+n(n+1)(n+2)=n(n+1)(n+2)(n+3)/4
6.1+3+6+10+15+.
=1+(1+2)+(1+2+3)+(1+2+3+4)+.+(1+2+3+...+n)
=[1*2+2*3+3*4+.+n(n+1)]/2
=n(n+1)(n+2)/6
7.1+2+4+7+11+.+ n
=1+(1+1)+(1+1+2)+(1+1+2+3)+.+(1+1+2+3+...+n)
=(n+1)*1+[1*2+2*3+3*4+.+n(n+1)]/2
=(n+1)+n(n+1)(n+2)/6
8.1/2+1/2*3+1/3*4+.+1/n(n+1)
=1-1/(n+1)=n/(n+1)
9.1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+...+n)
= 2/2*3+2/3*4+2/4*5+.+2/n(n+1)=(n-1)/(n+1)
10.1/1*2+2/2*3+3/2*3*4+.+(n-1)/2*3*4*...*n
=(2*3*4*...*n-1)/2*3*4*...*n
11.1^2+3^2+5^2+.(2n-1)^2=n(4n^2-1)/3
12.1^3+3^3+5^3+.(2n-1)^3=n^2(2n^2-1)
13.1^4+2^4+3^4+.+n^4=n(n+1)(2n+1)(3n^2+3n-1)/30
14.1^5+2^5+3^5+.+n^5=n^2 (n+1)^2 (2n^2+2n-1) /12
15.1+2+2^2+2^3+.+2^n=2^(n+1) – 1
不在其中的发给我.我给你算