Question

小学奥数题目,急!

(41+1/3)*3/4+(51+1/4)*4/5+(61+1/5)*5/6=
1-2/3-2/9-2/27-2/81-2/243-2/729=
能否告诉过程,非常感谢!

Answer 1

第一题：(41+1/3)*3/4=(40+1+1/3)*3/4=(40+4/3)*3/4=30+1=31
同理，式子=31+41+51+61=184
第二题：1-2/3=1/3=3/9
3/9-2/9=1/9=3/27
3/27-2/27=1/27=3/81
……
最后3/729-2/729=1/729

Answer 2

Answer 3

原题=41*3/4+51*4/5+61*5/6+1/4+1/5+1/6
=40*3/4+3/4+50*4/5+4/5+60*5/6+5/6+1/4+1/5+1/6
=30+40+50+1+1+1=123
原题=1/3-2/9-2/27-2/81-2/243-2/729
=1/9-2/27-2/81-2/243-2/729
=以此类推=1/729

Answer 4

1 原式=（123/3+1/3）*3/4+（204/4+1/4）*4/5+（305/6+1/5）*5/6
=124/3 * 3/4+ 205/4 * 4/5 + 306/5 * 5/6
=31+41+51=123
2 原式=1/3-2/9-2/27-2/81-2/243-2/729
=3/9-2/9-...
=3/27-..
=1/729