The sequence is defined as follows: A(n) = n/(n+1).

Question

The sequence is defined as follows: 

A(n) = n/(n+1).

How many of the first 100 terms of this sequence are less than 0.891

A) 7
B) 8
C) 9
D)10
E) 12

sumande · Answer

It is B.

A(9) = 0.9
A(8) = 0.89

Therefore, 8 terms are less than 0.891.

trahul4 · Answer

i used brute force method to arrive at the numbers 

1/2 , 2/3, 3/4, 4/5, 5/6 , 6/7 , 7/8, 8/9

all these are less than 0.891 .. others that follow inthis series are greater than 0.891. Hence B i.e 8 is the answer

raptr · Answer

OA is B) 8.

What I don't understand is how do you decide which term exactly is "the first term" and why  n  can't be 0 or negative.

If n=0 -> n/n+1 = 0/1 = 0 and 0<0.891

sumande · Answer

That question did pop in my mind. For n=-1, A(n) is undefined. For all other negative values of n, A(n) will be greater than 1. So, even considering negative integers won't make much of a difference. But as you rightly pointed out, n=0 does make a difference. Further the question does not even mention that n is an integer !! All in all, I believe that it is not a very well constructed question (if, of course, you have copied down the question completely ). Any other opinions ?? :-D

FN · Answer

No, it cant be B...cause we are not told if N is positive and greater than 0 or not..cause 0/1=0 which is less than 0.89 and thus the number should be 9...

I would say not knowing if N is positive and greater than 0...the number is 9 not 8...

any takers??

qtip · Answer

I initially looked at B) 8, but after looking for the typical GMAT traps, I tried A(0) ~ I think it should be C) 9 as well. In the GMAT, x/0 is undefined, but 0/x is not. right?

raptr · Answer

0/x i definitely not undefined. I picked "C" and it turned out to be the wrong answer. I tought I am missing something fundamental... obviously I am not. Or am I?

I copied the problem word for word. This is the explanation:

"Let's write out first 10 terms of this series: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11. Any subsequent element in this series is bigger than its predecessor. To answer the question we have to find the first element that is bigger than 0.891. It is the 9th element = 9/10 = 0.900; 8/9 = 0.888... is less than 0.891. Thus, there are only 8 elements in the whole series that are less than 0.891. "

As you can see, it doesn't consider n<1. 

I have no explanation. The official answer is B) This is question #3 from Challenge #14.

->>> I am not aware of a rule against posting Challenge materials here, but if there is such a rule and I am violating it, I appologize.

anonymousegmat · Answer

there is a rule, but don't worry... I had many problems with the challenges
as some of the answers/explanations are 'iffy'. I chose B - but everyone's objections are valid. I checked the GMAT OG math rules... it says the domain of a function can consist of only positive values and possible zero (not sure why we can't have negative values for a domain?)

so in this problem, i think unless the domain is restricted to positive values that answer is technically 9

The sequence is defined as follows: A(n) = n/(n+1).

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