Question

奥数题6年级1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40

Answer 1

1/1*2=1/1-1/2=(2-1)/1*2
所以得出1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+……1/39*40=
（2-1）/1*2+（3-2)/2*3+(4-3)/3*4+(6-5)/5*6+……（40-39）/40*39）=
1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6……1/38-1/39+1/39-1/40=
1/1-1/40=
39/40
所以答案为39/40

Answer 2

因为1/2=1-1/2
1/6=1/2-1/3
所以

原式=
1-1/2+1/2-1/3+1/3-1/4+................+1/38-1/39+1/39-1/40
=1-1/40
=39/40

Answer 3

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40
=1-1/2+1/2-1/3+...+1/39-1/40
=1-1/40
=39/40

Answer 4

1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/39-1/40
=1-1/40
=39/40