Another algebra

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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 -

    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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