校園小博士教育機構-分數分拆

1)1/4 + 1/28 + 1/70 + 1/130 + 1/208
= 1/4 + (1/3)(1/4 - 1/7) + (1/3)(1/7 - 1/10) + (1/3)(1/10 - 1/13) +
(1/3)(1/13 - 1/16)
= 1/4 + (1/3(1/4) - (1/3)(1/16)
= 1/4 + 1/12 - 1/48
= 12/48 + 4/48 - 1/48
= 15/48
= 5/16
2)1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
= 1/2 + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(6*7) + 1/(7*8)
= 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/6 - 1/7) + (1/7 - 1/8)
= 1/2 + 1/2 - 1/8
= 7/8


2009-10-09 23:22:09 補充：
= 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + 『(1/4 - 1/5)』 + (1/6 - 1/7) + (1/7 - 1/8)

correct to

= 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8)

Sorry!

2009-10-10 00:15:01 補充：
Missing something :

it should be

1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8)

Sorry!