8. A(k)=(-1)^(k+1)*(1/2^k), k=1, 2, …10, sum is between
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[确认]1/4—1/2
[思路]when k=1 ,A(k)=1/2
k=2,A(k)=-1/4
k=3,A(k)=1/8
....
k=10,A(k)=-1/2^10
so SumA(k) is more than 1/4 since -1/4<-1/4+1/8...+(-1/2^10)
and SumA(k) is less than 1/2 -1/4+1/8...+(-1/2^10)<0
My calculation for discussion:
The 10 numbers are:
1/2 , -1/4, 1/8, -1/16, 1/32, -1/64, 1/128, -1/256, 1/512, -1/1024
Sum =1/2 + 81/1024
=1/2 + 0.79
=0.579
since 0.579 is larger than 0.5 , therefore SUM cannot be less than 1/2. And I cannot figure out how do you get the 1/4 number? Please help.
15. PS: 1. if K is common multiple of75, 98 ,140, which of the following must be true?
Ⅰ. K is a multiple of 9
Ⅱ. K is a multiple of 49
Ⅲ. K is greater than 14000
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[确认]2
The factors for 75=3 x 5^2 x 7^2
98=2 x 7^2
140=2 x 5 x 7
Therefore, the least common multiple would be
2 x 3^2 x 5^2 x 7^2
=22050=K
Ⅰ. K is a multiple of 9
Ⅱ. K is a multiple of 49
Ⅲ. K is greater than 14000
Therefore K is a multiple of 9 ( I)
K is a multiple of 49 (II)
and k>14000 (III)
So all I, II, III are correct
Please advise.
Thank you.作者: bottle 时间: 2002-12-25 11:45
i think the least common multiple should be 2^2*7^2*5^2*3 so the ans should be 2and 3
what's the ans????作者: bottle 时间: 2002-12-25 11:45
i think the least common multiple should be 2^2*7^2*5^2*3 so the ans should be 2and 3
what's the ans????作者: mingja 时间: 2002-12-26 04:23
You are right : 75=5^2 x 3
140=2^2 x 5 x 7
Least common multiple is 2^2*7^2*5^2*3 =14700
Therefore K is NOT a multiple of 9 ( I)
K is a multiple of 49 (II)
and k>14000 (III)
So II, III are correct hopefully
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