1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45这个数学题?算

1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45这个数学题?算
1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45这个数学题?算

1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45这个数学题?算
1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45
=2*(1/6+1/12+1/20+1/30+1/42+...+1/90)
=2*(1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+...+1/9*10)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+...+1/9-1/10)
=2*(1/2-1/10)
=2*2/5
=4/5

答案4/5。用计算器算de。

1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
=(1/3+1/6)+(1/10+1/15)+(1/21+1/28)+(1/36+1/45)
=1/3(1+1/2)+1/5(1/2+1/3)+1/7(1/3+1/4)+1/9(1/4+1/5)
=1/3*3/2+1/5*5/6+1/7*7/12+1/9*9/20
=1/2+1/6+1/12+1/20
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/5
=4/5