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    Convergence testing of the series 1/(2^n-n)

    ystael: I thought long and hard about the comparison test, but the only thing I could think of to use as a comparison is \frac{1}{2^{n}}, which is greater than the original function, and it converges. i also tried variants of replacing 2 with other bases, and I found none that were either...
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    Convergence testing of the series 1/(2^n-n)

    Homework Statement Determine whether \sum\frac{1}{(2^{n}-n)} from n=1 to infinity converges or diverges. Homework Equations a_{n} converges if \stackrel{lim}{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_{n}}\right|<1. The Attempt at a Solution I'm really having a tough time knowing...
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    Power Series Representation of a Function when a is a polynomial

    Wow, I've got it now. I was making that way more difficult than it needed to be. Thanks so much for your help, you really elucidated the problem for me.
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    Power Series Representation of a Function when a is a polynomial

    I see. So I reworked the problem by differentiating f(x) with the numerator factored out, and the answer I got was (1+x)*\Sigma(-nx^{n-1}which is equal to \sum(-nx^{n-1}-nx^{n}, which is still drastically different to the answer given in the book. Is my answer right but reducible, or have I made...
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    Power Series Representation of a Function when a is a polynomial

    Power Series Representation of a Function when "r" is a polynomial Homework Statement Find a power series representation for the function and determine the radius of convergence. f(x)=\stackrel{(1+x)}{(1-x)^{2}} Homework Equations a series converges when |x|<1...
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    Block Attached to Pulley Question

    Homework Statement A 20-kg block with a pulley attached slides along a frictionless ledge. It is connected by a massless string through another pulley to a 5.0-kg block which hangs off the ledge. Find (a) the acceleration of each block, and (b) the tension in the connecting string...
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