Maths

用等比數列來計算~
公式等比無限項之和的公式:
S = a/(1-R)

0.206060606060....=0.2+(0.006+0.00006+0.0000006+0.000000006......)
=0.2+ 0.006/(1- 0.01) 首項a=0.006 公比R=0.01
=0.2+ 6/990
=198/990 + 6/990
=204/990
=102/495



2008-10-26 20:45:26 補充：
再化簡= 34/165

Let 0.20606060... = x
100x = 20.606060...
100x - x = 20.606060... - 0.20606060....
99x = 20.4
x = 20.4/99 = 204/990 = 102/495= 34/165.