You might want to take a look through
http://www.wolfram.com/language/fast-introduction-for-programmers/interactive-usage/
to get a sense of how to do a variety of things in Mathematica and what the syntax is for, for example, creating functions based on patterns, plotting functions, generating tables of values from functions and so on.
To get your started, you can create functions based on the results generated by your RSolve examples using something like this
xValue[n_Integer,
r_, \[Alpha]_, {x0_, b0_}] /; (0 < r < 1 && \[Alpha] >= 1) :=
1/(1 + r - \[Alpha]) ((1 + r)^n x0 +
r (1 + r)^n x0 - (1 + r)^n x0 \[Alpha] +
b0 (1 + r)^n \[Alpha] UnitStep[-1 + n] -
b0 \[Alpha]^(1 + n) UnitStep[-1 + n]);
bValue[n_Integer, \[Alpha]_, b0_] /; (\[Alpha] >= 1) := b0 \[Alpha]^n;
Then, for example you will get:
In[24]:= xValue[10, 1/2, 1, {5000, 400}]
Out[24]= 42708125/128
In[27]:= bValue[10, 1, 400]
Out[27]= 400
Or
In[28]:= N[xValue[10, 1/2, 1, {5000, 400}]]
Out[28]= 333657.
You could create a table of xValues like this
In[30]:= Table[{n, N[xValue[n, 1/2, 1, {5000, 400}]]}, {n, 0, 10}]
Out[30]= {{0, 5000.}, {1, 7900.}, {2, 12250.}, {3, 18775.}, {4,
28562.5}, {5, 43243.8}, {6, 65265.6}, {7, 98298.4}, {8,
147848.}, {9, 222171.}, {10, 333657.}}
And so on.... you could use Grid to format it, or TableForm if you want a quick and dirty tabular view.
