1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/50+2/50+...+49/50)
来源:百度知道 编辑:UC知道 时间:2024/04/28 05:36:33
1/n+2/n+……+(n-1)/n
=(1+2+……+n-1)/n
=[n(n-1)/2]/n
=(n-1)/2
所以1/2=(2-1)/2=1/2
1/3+2/3=(3-1)/2=2/2
1/4+2/4+3/4=(4-1)/2=3/2
……
1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/50+2/50+...+49/50)
=1+1/2++2/2+3/2+4/2+……+50/2
=1+(1+2+……+50)/2
=1+(50*51/2)/2
=1+1275/2
=1277/2
=1 + 1/2 + 1 + (1+1/2) + 2 + (2+1/2) + …… + (25+1/2)
=1 + (1/2+25+1/2)*49/2
=638
1/n+2/n+...+(n-1)/n=n*(n-1)/2/n=(n-1)/2
1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/50+2/50+...+49/50)
=1+(1+2+...+49)/2
=1+49*50/2
=1226
对任意n
若n为奇数,则1/n+2/n+……+(n-1)/n=(n-1)/2,(高斯求和)
若n为偶数,则1/n+2/n+……+(n-1)/n=(n-2)/2+1/2,(高斯求和)
故
1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/50+2/50+...+49/50)
=1+1/2+1+(1+1/2)+2+(2+1/2)+……+24+(24+1/2)
=1+(1+2+...+24)*2+1/2*25
=613.5
612.5
363.5
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1+1/2+1+1/3+1+1/4+......+1/100=?
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
(1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2)
1/1+1/2+1/3+1/4+。。。。+1/N 是多少
1/1+1/2+1/3+1/4+......1/2002=?
1-1/2+1/3-1/4+........1/99-1/100
求和Sn=1+(1+1/2)+(1+1/2+1/4)+....+[1+1/2+1/4.....+1/2^(n-1)]
数列 1+(1+1/2)+(1+1/2+1/4)+..............=?