Question

1/2+(1/3+2/3)+(1/4+2/4+3/4)+……+（1/50+2/50+3/50+……+48/50+49/50)

Answer 1

规律：第n组分母为n+1，分子从1加到n。
1/(n+1)+2/(n+1)+...+(n-1)/(n+1)=(1+2+...+n)/(n+1)=[n(n+1)/2]/(n+1)=n/2
本题中共50-1=49组。
1/2 +(1/3+2/3)+...+(1/50+2/50+...+49/50)=(1+2+...+49)/2=49×50/2=1225

Answer 2

1/2+(1/3+2/3)+(1/4+2/4+3/4)+……+（1/50+2/50+3/50+……+48/50+49/50)
=1/2+2/2+3/2+……+49/2
=（1/2+49/2）×49/2
=25×49/2
=612.5

Answer 3

原式=1/2+3/3+6/4+.........+1/2乘以50
=1/2+1+3/2+............+1/2乘以50
=1/2（1+2+3+4+........49）
=1/2乘以1225
=612.5

Answer 4

1/2+(1/3+2/3)+(1/4+2/4+3/4)+…+(1/50+2/50+3/50+…+48/50+49/50)
=1/2+(2*3)/6+3*4/8+4*5/10+….+49*50/100
=1/2+2*(1/2)+3*(1/2)+4*(1/2)+…+49*(1/2)
=1/2(1+2+3+…+49)
=(1/2)*(49*50)/2
=1225/2
=612.5