Statistics/Probability/Finance help motivate EGs in calc, esp. of
series and stuff.

Esp. net present value and such.

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Here's a cute one:
$\sum \frac{n}{2^n}=2$
More generally,
$\sum \frac{n}{r^n}=r$
and
$\sum \frac{n}{r^{n+1}}=1$
Here's a way to interpret them:
- functionally
  This is just the power series for $1/(1-x/r)^2$ or such.

- probability
  Given a sequence of bernoulli trials (coin flips),
  the likelihood that a given flip is the first member of a streak of
  length $n$ is $1/2^{n+1}$.
  EG, for length 1, must have previous -and- next be different,
  so 1/4. For length 2, need 3 flips, so 1/8, etc.
  However, there are $n$ coins in each streak of length $n$,
  so $n/2^{n+1}$ is likelihood that you're in a streak of length $n$.
  [is this a Poisson distribution?]
  Adding these up yields $1$, since it's a probability distribution.
  [yes, obviously this is only asymptotic: for a finite length there's
  a slight adjustment b/c can't have very long streaks, thus shorter
  streaks a -little- more likely, etc.]
