Question

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法

Answer 1

小学的解法不是很确定，不知小学生知不知道 1+2+3+....+100=100(100+1)/2?

如果知道就好办了

1=2(1-1/2)
1/(1+2)=2(1/2-1/3)
...
1/(1+2...+100)=2/(100*101)=2(1/100 -1/101)

1+1/(1+2)+1/(1+2+30+....1/(1+2+....+100)=2(1-1/101)=200/101

Answer 2

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)
=2/(1×2)+2/(2×3)+2/(3×4)+........+2/(100×101)
=2[1/(1×2)+1/(2×3)+1/(3×4)+.........+1/(100×101)]
=2(1-1/2+1/2-1/3+1/3-1/4+.........+1/100-1/101)
=2(1-1/101)
=200/101

Answer 3

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)
=1＋1/3＋1/6＋1/10＋．．．．＋1/5050
y＝2/｛x×（x＋1）｝＝2[1/x-1/(x+1)]
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+......+1/(1+2+3+...+100)
=2[(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/100-1/101)]
=2(1-1/101)
=200/101

Answer 4

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=2/1*2+2/2*3+2/3*4+2/4*5+……+2/100*101
=2[1-1/2+1/2-1/3+……+1/100-1/101]=2(1-1/101)=200/101

Answer 5

高中等差求和加裂项求和，不解释