求助

xiaochan1982

求助新的模考软件两道数学题,等比公式忘了

Q1, a certain jar contains only B black marbles, W white marbles, and R red marbles, if one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that marble chosen will be white?

1, r/(B+W)> w/(B+R)

2, B-W > R

key:A

Q2, 2+2+2^2+2^3+2^4+…..+2^8=?

Key: 2^9

thanks

smilinglan

Q1, a certain jar contains only B black marbles, W white marbles, and R red marbles, if one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that marble chosen will be white?

1, r/(B+W)> w/(B+R)

2, B-W > R

key:A

题目是问 R/(B+W+R)>W/(B+W+R),因为B,W,R都为正整数,也即是求R>W

条件一 R/(B+W)> W/(B+R)

可推出 R/(B+W) - W/(B+R) >0

[ R(B+R)-W(B+W)]/(B+W)(B+R) >0

(R-W)(R+W+B)/(B+W)(B+R) >0

因为B,W,R都为正整数,所以(R+W+B)>0,(B+W)(B+R)>0

推出R-W>0

所以条件一单独充分

条件二单独不充分

选A

Q2, 2+2+2^2+2^3+2^4+…..+2^8=?

Key: 2^9

此题用等比数列求和公式可轻松解决

thanks

meimei5656

第二题把各项都提出一个2^8得到2^8（2^-7+2^-6+2^-5+2^-4+2^-3+2^-2+2^-1+2^0)

后面括号得值为2 因为2^0为1 剩下的近似等于1按照等比数列的求和公式

这样最后等于2^9次方