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...
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...
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.
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...
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...
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...