Timmy is tired. He does not want to add all the infinite terms of $\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 } + \dots$So instead, he just adds the first three terms.

1. How far is his result from the actual sum of the infinite series? (This is called his "error.")

   Hint (a):

   For an infinite geometric series:

2. What would his error have been if he added the first four terms?

3. Generalize his error. That is, if he adds up $n$ terms of this geometric series, what will his error be?

   Hint (c):

   For a finite geometric series:
   Substitute $a =\frac{1}{2}$ and $r =\frac{1}{2}$ into the formulas in the hints then evaluate.