deletions | additions       diff --git a/beginproblem__Consid.tex b/beginproblem__Consid.tex  index 1b6b5dc..e98d76d 100644  --- a/beginproblem__Consid.tex  +++ b/beginproblem__Consid.tex 
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\\ \\  $Z_n = (1 - \frac{2 -\sqrt{2}}{-2\sqrt{2}})(1+\sqrt{2})^n + (\frac{2 -\sqrt{2}}{-2\sqrt{2}})(1-\sqrt{2})^n$  \\*  \\ \\ \\  \begin{problem}  Solve the following recurrence equation: 
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\\  $\alpha _3 = \frac{8}{5}+\frac{11}{5\sqrt{2}}$  \\ \\  The solution is:  \\  $V_n = (-\frac{4}{5}-\frac{11}{5\sqrt{2}}-\frac{2-2(\frac{8}{5}+\frac{11}{5\sqrt{2}})+\sqrt{2}(\frac{8}{5}+\frac{11}{5\sqrt{2}})}{2+\sqrt{2}})(-1)^n+\frac{2-2(\frac{8}{5}+\frac{11}{5\sqrt{2}})+\sqrt{2}(\frac{8}{5}+\frac{11}{5\sqrt{2}})}{2+\sqrt{2}}(1+\sqrt{2})^n+\frac{8}{5}+\frac{11}{5\sqrt{2}}(1-\sqrt{2})^n-\frac{2}{5}n - \frac{4}{5}$  \\  \\*