所有分母为偶数的分数一共有10组，全部相加应该是10*（1/2）+1+2+3+....+9=5+4*10+5=50
所有分母为奇数的分数一共有9组，例如1/5+2/5+3/5+4/5=(5-1)/2=2，所以全部分母为奇数的分数相加应该是1+2+3+.....+9=45
原式=50+45=95
1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/20+2\/20+3\/20+.+19\/20)=...
分母为偶数（2,4,6,8,……,20）,例如1\/4+2\/4+3\/4=(4-2)\/2+1\/2=1+1\/2；所有分母为偶数的分数一共有10组,全部相加应该是10*（1\/2）+1+2+3+.+9=5+4*10+5=50所有分母为奇数的分数一共有9组,例如1\/5+2\/5+3\/5+4\/5=(5-1)\/2=...
...+2\/20)+(3\/4+3\/5…+3\/20)+…+(18\/19+18\/20)+19\/20
=1\/2+（1\/3+2\/3）+（1\/4+2\/4+3\/4）+……+（1\/20+2\/20+……+19\/20）=（1+2+……+19）\/2 =95
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 ...
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)n\/(2n)=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) 简算_百度...
因为(1+2+...+(n-1))\/n=[n(n-1)\/2]\/n=(n-1)\/2 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\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/40+2\/40+...+38\/40+39\/40)_百度...
则上面的式子为0\/1+1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/60+2\/60+3\/60+...+59\/60)观察对于上面的第n项,分子为n(n-1)\/2 分母为n,则第n项f(n)=(n-1)\/2=n\/2-1\/2,那么对于上面60项之和 S(60)=(1\/2-1\/2)+(2\/2-1\/2)+(3\/2-1\/2)+..+(60\/2-1\/2...
1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/100+2\/100...+98\/100+99\/100...
1\/3+2\/3=1\/2×（3-1）1\/4+2\/4+3\/4=1\/2×（4-1）...原式=1\/2×（2-1）+1\/2×（3-1）+1\/2×（4-1）+...+1\/2×（100-1）=1\/2×（1+2+3+...+99）=1\/2×（1+99）×99×1\/2 =1\/4×100×99 =25×99 =2475 ...
...1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+···+(1\/10+2\/10+···9\/10)_百 ...
计算每一项：1\/k+2\/k+..+(k-1)\/k=1\/k*[1+2+..+(k-1)]=1\/k*k(k-1)\/2=(k-1)\/2 所以1\/2+(1\/3+2\/3)+（1\/4+2\/4+3\/4）+···+（1\/10+2\/10+···9\/10）=1\/2+2\/2+3\/2+..+9\/2 =1\/2*(1+2+..+9)=1\/2*9*10\/2 =45\/2 （1+1\/2）*（1+1\/...
1\/2+(1\/3+2\/3)+(1\/4+2\/4+3\/4)+...+(1\/40+2\/40+...+39\/40)
原式=1\/2+（1+2）\/3+（1+2+3）\/4+（1+2+3+4）\/5+...+（1+2+3+4+5+6+..+39）\/40 =1\/2+[（1+2）*2*1\/2]\/3+[(1+3)*3*1\/2]\/4+[(1+4)*4*1\/2]+...+[(1+39)*39*1\/2]\/40 =1\/2+2*1\/2+3*1\/2+4*1\/2+5*1\/2+...+39*1\/2 =1\/2*(1+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
