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Calculus and Beyond Homework Help
The number of times the function vanishes
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[QUOTE="brmath, post: 4533647, member: 486151"] If x < 1 this sum consists entirely of negative terms, so will have not zeros in that range. Suppose n < x < n+1. Then all the terms up to n/(x-n) will be positive and all the rest will be negative. It seems that there may be an x where the positive and negative terms cancel. If there is such an x, it must be the only one, because making it larger will make create more positive terms and fewer negative terms, and making it smaller vice versa. Can you formalize a way to say this? Could it be that there is no such x? Why or why not? [/QUOTE]
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The number of times the function vanishes
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