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What is the scope including 1/11+1/12+1/13+......+1/20?

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What is the scope including 1/11+1/12+1/13+......+1/20?

by Max@Math Revolution » Sun Jul 24, 2016 2:09 am
What is the scope including 1/11+1/12+1/13+......+1/20?
A 1/6~1/5
B. 1/5~1/4
C. 1/4~1/3
D. 1/3~1/2
E. 1/2~1

*An answer will be posted in 2 days.
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by AbdurRakib » Sun Jul 24, 2016 5:28 am
Max@Math Revolution wrote:What is the scope including 1/11+1/12+1/13+......+1/20?
A 1/6~1/5
B. 1/5~1/4
C. 1/4~1/3
D. 1/3~1/2
E. 1/2~1

*An answer will be posted in 2 days.
Definitely ,1/11 has the greatest value among all 10 numbers,so if all numbers would equal to 1/11 the highest sum would be 10*(1/11)=10/11,which is slightly less than 1

And 1/20 has the lowest value among all 10 numbers,so if all numbers would equal to 1/20 the lowest sum would be 10*(1/20)=1/2

so the range of the sum is between 1/2 and 1
So,correct answer E
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by Max@Math Revolution » Mon Jul 25, 2016 6:32 pm
The sum of a sequence of reciprocals is determined by the first and the end term. So, since 1/2=10/20<1/11+1/12+1/13+......+1/20<10/11<10/10=1, the correct answer is E.
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