1/(n+1)

Question

1. 1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n. What is n?

Raffie · Answer

Can't do the long division too quickly. But 1/31 + 1/32 +1/33 must be about 3/32, or a little bit less than 1/10 (3/30) and greater than 1/11 (3/33). So I'd say that n is 10, n+1 is 11.

combres · Answer

I see your logic getting to 3/32, but because 1/(n+1) is less than 1/n, I think n should be 9. 


1/10< 3/32 <1/9 

yesh?

Ferihere · Answer

Isn't it 341>n>340

or there should be single value???

mastergmat1 · Answer

1/3 = 0.333

1/ 30 = 0.0333

1/31 < 0.033 = 0.032

1/32 < 0.031 = 0.031

1/33 < 0.031 = 0.030 

sum = 0.093

1/11 < 0.093 < 1/n+1 


Cant figure out after this!!

Ravshonbek · Answer

What if we do this:

(1-30/31)+(1-31/32)+(1-32/33)=3-2.88=.12
30/31=.96 and so others
so

1/(n+1)<12/100<1/n
from here the only 
i think there might not be exact integer to replace it. but this range might do:
1/(n+1)<3/25
3/25<1/N
from there we should find the range only. 
since it is an inequality, we cannot say that it is exactly this number, what actually are answer choices?

1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n. What is n

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