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Let [itex]f:[0,1]->ℝ[/itex] and [itex]f(x) = \frac{1}{n}[/itex] when [itex]x=\frac{1}{n²}, n=1,2,...[/itex] and 0 in other case.

Define such spacing/interval [itex]D[/itex] that [itex]S_D-s_D < \frac{1}{100}[/itex]. Here [itex]S_D[/itex] refers to the upper sum and [itex]s_D[/itex] the the lower sum.

Now, i'm not sure how to approach this really since the sum is defined so that the values of x jump a different interval every time. Any help would be appreciated. Hopefully i managed to explain the problem clearly enough.

Define such spacing/interval [itex]D[/itex] that [itex]S_D-s_D < \frac{1}{100}[/itex]. Here [itex]S_D[/itex] refers to the upper sum and [itex]s_D[/itex] the the lower sum.

Now, i'm not sure how to approach this really since the sum is defined so that the values of x jump a different interval every time. Any help would be appreciated. Hopefully i managed to explain the problem clearly enough.

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