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    Riemann integrability

    The problem states: Decide if the following function is integrable on [-1, 1] f(x)=\left\{{sin(\frac1{x^2})\;\text{if}\;x\in[-1,\;0)\cup(0,\;1]\atop a\;\text{if}\;x=0} where a is the grade, from 1 to 10, you want to give the lecturer in this course What I don't understand is how to find L(f...
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    What is the difference between an electron and electromagnetic waves?

    Both are energy right? I'm asking cause I'm trying to understand the double-slit experiment and I'm just wondering how they can be sure to treat the electron as a particle. Could it be performed with for instance whole atoms or maybe the cores or something else that's more obviously matter...
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    Hello, can anyone tell me how I can show that this

    Hello, can anyone tell me how I can show that this diverges \int_{-1}^0\frac{e^x}{x+1}dx I'm out of ideas
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    Sum as formula

    How can I show that \sum_{i=1}^n\;\frac1{i(i+1)}=\frac{n}{n+1} I've already figured out i can write it as \sum_{i=1}^n\;\frac1{i}-\sum_{i=1}^n\;\frac1{i+1} but as I'm a little drunk I can't figure out how to get from there to the formula. Sorry if I put this in the wrong sextion, but...
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    Infinite sum

    \sum^k_{n=1}e^{-n\sum^k_{n=2}...e^{-n\sum^k_{n=k-1}e^{-n}}} Can anyone help me find out if this converges and if so how to calculate the sum? I don't have an idea on how to even start. This is not homework