数学总结12.16-12.22讨论

mingja

8. A(k)=(-1)^(k+1)*(1/2^k), k=1, 2, …10, sum is between ------------------- [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 ------------------------------------ [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.

bottle

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????

bottle

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????

mingja

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