Posted by **Elle** on Tuesday, January 20, 2009 at 3:33pm.

Determine the number of positive integers n that satisfy:

1/2 < n/n+1 < 99/101

I don't know how to solve this besides plugging in random numbers, which would take all day. Any other suggestions for a faster way to solve it?

Thank you!

- Another algebra -
**drwls**, Tuesday, January 20, 2009 at 4:44pm
The smallest number that satisfies

1/2 < (n/n+1) is 2/3

The largest number that satisfies

n/(n+1) < 99/101 is 49/50.

Here's proof of that:

49/50 = 0.980000

99/101 = 0.980198

50/51 = 0.98039

So all n/(n+1) numbers in the series

2/3, 3/4, 4/5 ... 49/50 satisfy the inequality.

There are therefore 48 numbers n that satisfy the condition.

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