I want to ask...

Find1-2+3-4+5-6+7-8+ ...+9 999-10000.

It can be seen that for every pair of numbers (1st and 2ns, 3rd and 4th,…..9999th and 10000th), the sum = -1.

Also, no. of pairs = 10000 /2 = 5000

Thus, the sum : 1-2+3-4+5-6+7-8+ ...+9 999-10000 = (-1) * 5000 = -5000 (ans.)

Find(-1)*(-2)*(-3)*( -4)*...*(-100) / (+2)*(+3)*(+4)*...*( +100)
( * = times and / =divide)

It can be seen that the numerator : (-1)*(-2)*(-3)*( -4)*...*(-100) has 100 –ve signs, i.e. even times

Recall 負負得正, therefore, the product sum of the numerator is +ve

Therefore, the value numerator = the value of the denominator
That is, (-1)*(-2)*(-3)*( -4)*...*(-100) / (+2)*(+3)*(+4)*...*( +100) = 1 (ans.)


2007-09-15 20:32:17 補充：
幫到你嗎?

1-2+3-4+5-6+7-8+ ...+9 999-10000 = (-1) * 5000 = -5000

(-1)*(-2)*(-3)*( -4)*...*(-100) / (+2)*(+3)*(+4)*...*( +100) = 1