Recent content by utopiaNow

Thank you for the help!

Interesting, so everything seems to be canceling out if you keep going long enough diagonally, except the 1/4 in the second row. However is there any way to formalize this? Or is simply noticing this pattern enough for a formal proof?

Hi, I tried doing that originally, but I don't see any patterns that I can exploit when I write the terms of the partial decomposition for n = 1, 2, 3,..., N-2, N-1, N as you stated. Do you have any further suggestions?

Homework Statement Use partial fractions to show \displaystyle\sum_{n=1}^\infty \frac{1}{n(n+1)(n+2)} = \frac{1}{4} The Attempt at a Solution I did the partial fraction decomposition to get: \displaystyle\sum_{n=1}^\infty \frac{1}{2n} - \frac{1}{n + 1} + \frac{1}{2n + 4} I'm not...

Thanks guys for the help. You guys are right about talking to the profs. I will inquire more about this at my school. And you're right about the lack of funding. Thanks again for the input.

Alright here's my story, I wanted to apply for undergraduate research positions this summer related to some astrophysics, however I didn't get any callbacks (not sure why, my grades are fine, my guess would be, being a math major I lost out to too many physics students applying, it is pretty...

Homework Statement Suppose that the stars in a disk galaxy have a constant orbital speed v out to the edge of its spherical dark halo, at a distance R_{halo} from the center of the galaxy. 1. What is the average density \rho for the galaxy, including its dark halo? 2. If a bound structure...

Homework Statement We are to assume the recombination happens at redshift z_{rec} when the number density of photons n_{\gamma}(z_{rec}) capable of ionizing hydrogen is exactly equal to the number density of baryons n_{b}(z_{rec}) . Use the measured number density of baryons, the...