LaTex input (not so pretty) vs LaTex output = Pretty math

Thanks all!

The forum also has built in tags which allows use of subscripts and superscripts withouth knowledge of latex:

Hi!

Suppose that a   is a constant and r is not zero or one and for each n in {1,2,3,...}
                     0
                                                    n
a   = r*a     .    Show that a  = a * r    for each n in {1,2,3,...}.
  n         n-1                      n     0
                                                             1
For n=1 we have a  = r*a     = r*a  = a *1  .   So it works for n=1.
                           1        1-1        0     0

Now suppose that for some positive integer k,

                          k                                                               k               k          k+1
we have a  = a *r  .   Then  a      = r*a           = r*a   = r*a *r  = a * r * r   = a*r
               k     0                   k+1        (k+1)-1        k         0         0                0

So given that it works for k we have shown that it works for k+1, which is the inductions step.
Therefore it works for all n in {1,2,3,...}.

Is there any way to put this page into a half-space mode?  Then the super and subscripts would
look pretty nice. 

Let a(sub0) and r be fixed real numbers with r ≠ 0 and r ≠ 1, and suppose that for each n ∈ N, a(subn) = r*a(subn-1).

For every nonnegative integer n, a(subn) = a(sub0) * r^n.

Prove by induction.