mathie

I'm trying to understand this concept.

Suppose one light object in motion hits a heavier stationary object, but the latter does not move. If there is no work being done on the heavier object, where did the kinetic energy that the light object had transfer to?

Here's an example for a countably infinite expression.

e.x. What is the sum of all positive integers divided by the square of the amount of positive integers?

1+2+3+4+5+6+...

----------------------------

(1+1+1+1+1+1+...)^2

Then the limit is

lim(n->inf) (1+2+3+...+n)/n^2

=lim(n->inf) (n(n+1)/2)/n^2

=lim(n->inf) (n^2+n)/2n^2

=lim(n->inf) 1/2+1 / 2n

=1/2

How would you do, for example, the sum of all real numbers between 0 and 1 inclusive, divided by the square of the amount of such numbers?

Just trying to get a basic idea. How much air resistance is there on a descending sphere (1 kg)when there's no wind?