數學難題一問(20分)急!

log 1 + log 2 + log 3 + ... + log 99 + log100
= log (1)(2)(3)(4)(...)(99)(100) (因為log m + log n = log mn)
= log 100! (因為1x2x3x4x5...x(n-2)(n-1)n = n!)

log1 = 0
log 10 = 1
log 100 = 2
所以log 1 - log 100入面每一個既值都係0-2中間
所以
91 < log 1 + log 2 + log 3 + ... + log 99 + log100 < 189
自己計埋落去啦 = =

2008-04-11 00:44:09 補充：
91 < log 1 + log 2 + log 3 + ... + log 99 + log100 < 189

log 1+log 2+log 3+ log4.......+ log 100
=log 1*2*3*......*100
(log m+log n=log mn)
=log (100-99)*(100-98)*(100-97)*...*100
=log 100*(100-1)*(100-2)*(100-3)*...*(100-99)
[n!=n(n-1)(n-2)(n-3)........]
=log 100!