Homework Statement
Write the following expression in a simpler form:
$\sum_{1}^{n} F_{2i} \cdot F_{2i-1}$
It doesn't have to be closed-form, probably something on the line of:
$\sum_{0}^{n} F_{i}^{2} = F_{n} \cdot F_{n+1}$
(We define the sequence the ususal way, starting the indexing from 0...
If you don't know what potential energy or kinetic energy is, just solve it with your original idea. Also read http://en.wikipedia.org/wiki/Kinetic_energy and http://en.wikipedia.org/wiki/Potential_energy :smile:
Otherwise...
kinetic energy + potential energy = constant
because energy is...
I think you don't have enough information.
The crucial piece of the puzzle that's missing is how long the 50N force was applied? 0.01 seconds? 0.1 seconds? It makes a difference.
Without that, you can't determine the change in momentum, from which you may deduce the starting velocity v0...
Homework Statement
You have a thin lens with a concave and a convex side (let's say with radii r and R). You also have 2 mirrors, a convex one, that fits perfectly into the lens' concave side, and a concave one, that fits perfectly onto the lens' convex side (so the corresponding radii of...
Hi!
If I understand correctly, then
sin\left(\sqrt{n}\right)
is what you are looking for. The proof is based on the idea sin(a)-sin(b) < a-b and sqrt(n+1)-sqrt(n) converges to 0.
I originally bumped this post, because I need help with a similar problem, where not
an+1-an converges to 0...