小学6年级算数题一

1/(1×2) = 1/1 - 1/2
1/(2×3) = 1/2 - 1/3
...
1/(42×43) = 1/42 - 1/43

所以：
1/1×2)＋1/(2×3)＋1/(3×4)＋1/(4×5)＋......＋1/(42×43)
=(1/1 - 1/2) + (1/2 - 1/3) + ... + (1/42 - 1/43)
=1 - 1/43
= 42/43

1/（1×2)＋1/(2×3)＋1/(3×4)＋1/(4×5)＋......＋1/(42×43)
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）＋......+（1/42-1/43）
=1-1/43
=42/43

1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
.
.
.
1/(42*43)=1/42-1/43

所以原式=1-1/2+1/2-1/3+....-1/42+1/42-1/43=1-1/43=42/43