数列求和1/13,1/24,1/3*5...1/n(n+2)RT

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 02:22:26

数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)RT
数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)
RT

数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)RT
1/1*3=(1/2)(1-1/3)
1/2*4=(1/2)(1/2-1/4)
...
1/n(n+2)=(1/n - 1/(n+2))/2
原式=(1/2)(1-1/3+1/2-1/4+...+1/(n-1)-1/(n+1)+1/(n)-1/(n+2))
=(1/2)(1+1/2-1/(n+1)-1/(n+2))
=3/4-(2n+3)/2(n+1)(n+2)

an
=1/(2n-1)(2n+1)
=1/2[1/(2n-1)-1/(2n+1)]
Sn
=1/2[1-1/3]+1/2[1/3-1/5]+1/2[1/5-1/7]+...+1/2[1/(2n-3)-1/(2n-1)]+1/2[1/(2n-1)-1/(2n+1)]
=1/2[1-1/3+1/3-1/5+1/5-1/7+...+1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=n/(2n+1)

1/n(n+2)=(1/n - 1/(n+2))/2

1/n(n+2)=(1/2)[1/n-1/(n+2)] 原式=[1+1/2-1/(n+1)-1/(n+2)]/2

1/（1+2+3+4+.+n）数列求和数列1/(2n-1)(2n 3)怎么求和数列求和 1+3+5+.+（2n-1） An=4/(n+1)(n+3)数列求和高中数列求和s=1!+2!+3!+...+n! 数列求和3+5+7+...+2n-1 高二数列求和求和1/(1*3)+1/(2*4)+1/(3*5)+……+1/[n(n+2)] 问道数列求和题1+1/2+1/3+1/4+.+1/n 求和该怎么求啊? 差比数列求和(2^(N+1))*N求和数列求和用分组求和及并项法求和 Sn=1^2-2^2+3^2-4^2+…+(-1)^(n-1)·n^2 数列求和S(n)=∑(1/x^2)怎么算～帮帮x=1,2,3,4,……,xx为自然数～数列求和数列1/（2n+1)的求和? 数列1,4,12,32,80……数列求和数列求和：1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+4+n) 数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)RT 数列求和 1/1*2+1/2*3+1/3*4+..+1/9*10 数列求和 1/1*2+1/2*3+1/3*4+...+1/9^10 数列求和 1+1/2+1/3+1/4+1/5+……1/99=?