1/2+（1/3+2/3）+（1/4+2/4+3/4）+（1/5+2/5+3/5+4/5）+...+（1/50+2/50+3/50+...+49/50）=
0.5 + 1 + 1.5 +2 + 2.5 + 3 + .... +24 + 24.5=
（0.5+24.5） + （1 + 24）+（1.5+23.5）+（2+23）+...+(12+13)+12.5=
25*24+12.5=612.5
=(1+2+3+4+5+······+49)/2
=612.5
利用等差数列求和公式。找通项。
1/n+2/n+3/n+······+(n-1)/n
=(1+n-1)x(n-1)/2n
=（n-1）/2
所以原式化简为1/2+2/2+3/2+4/2+5/2+······+49/2追问
3Q
...+(1\/4+2\/4+3\/4)+...(1\/50+2\/50+3\/50+...+49\/50)的简便运算
找出通项为（n-1+1）*（n-1）\/2n即为（n-1）\/2 然后用等差公式=49*50\/4=1225\/2
1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/50+2\/50+...+49\/50) 简算
所以1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/50+2\/50+...+49\/50)=1+1\/2+2\/2+...+49\/2 =1+(1+2+3+...+49)\/2 =1+49*50\/2*1\/2 (1+2+……+n=n(n+1)\/2)=1+1225\/2 =1227\/2
1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/50+2\/50+...+49\/50)分数的简便...
1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/50+2\/50+...+49\/50)=1+1\/2+2\/2+...+49\/2 =1+(1+2+3+...+49)\/2 =1+49*50\/2*1\/2 =1+1225\/2 =1227\/2
1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+……+(1\/50+2\/50+3\/50+……+49\/50) 十 ...
=1\/2+(1\/3+2\/3)+...+(n-1)\/2 =(1+2+...+49)\/2 =(1+49)*49\/4 =1225\/2;
1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/50+2\/50+...+49\/50)等于多少...
解：原式 =1+1\/2+1+6\/4+……+49×25\/50 =1+1\/2+2\/2+3\/2+……+49\/2 =1+(1+2+3+……+49)\/2 =1+(1+49)×49÷2\/2 =1+50×49÷4 =613.5
1\/2+1\/3+2\/3+1\/4+2\/4+3\/4+……+1\/50+2\/50+3\/50+……+49\/50
分母为n+1,分子为1+2+...+n=n(n+1)\/2 分数和为n\/2 1\/2+1\/3+2\/3+1\/4+2\/4+3\/4+……+1\/50+2\/50+3\/50+……+49\/50 =(1+2+3+...+49)\/2 =612.5
1\/2+1\/3+2\/3+1\/4+2\/4+3\/4+1\/5+2\/5+3\/5+4\/5+...+1\/60+...+59\/60
所以原式=1\/2+2\/2+3\/2+……+59\/2 =(1+2+……+59)\/2 ＝（1+59）*59\/2\/2 =885 回答者： 小南VS仙子 - 高级魔法师 七级 9-17 17:39 1\/2+（1\/3+2\/3）+（1\/4+3\/4）+2\/4+（1\/5+4\/5）+（2\/5+3\/5）+...+(29\/60+31\/60)+30\/60= 从3数起，有58个数，...
1\/2+1\/3+2\/3+1\/4+2\/4+3\/4...+1\/50+2\/50+...48\/50+49\/50=?
1\/2+1\/3+2\/3+1\/4+2\/4+3\/4...+1\/50+2\/50+...48\/50+49\/50 ①1\/2+2\/3+1\/3+3\/4+2\/4+1\/4...+49\/50+48\/50+...2\/50+1\/50 ②仔细观察2式,可发现2式相同,所以将2式相加然后除以2就可求出值是多少因为上下2式对应项的和都为1,...
1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+(1\/5+2\/5+3\/5+4\/5)+……+(1\/50+2\/50...
仔细观察，这个是一个等差数列 第一项1\/2 第二项1 第三项3\/2 第四项2 .……最后一项49\/2 一共49项，结果等于49×（1\/2+49\/2）\/2=1225\/2=612.5
1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/50+2\/50+...+49\/50)
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 ...
