Help with recurrence relation It 's been a long time since I touched this kind of math , so please help me to solve the relation step by steps : 
$V_k = (1+i)*V_{k-1}+P$ 
I know the answer is  $V_k = (P/i)*((1+i)^k-1) $ 
Thanks in advance.

Another general approach: to get rid of the constant write the second equation (denote $1-i=r$ for simplicity).
$$
V_{k-1}=r V_{k-2}+P
$$
Now subtract it from the first expression. You get (denote $\Delta V_{k}=V_{k}-V_{k-1}$):
$$
\Delta V_{k}=r \Delta V_{k-1}=r^2\Delta V_{k-2}=\ldots =r^{k-1}\Delta V_{1}
$$
Now sum over $k$ on both sides. On LHS you get a telescoping sum:$\sum_{k=1}^{n}\Delta V_{k}=V_{n}-V_{0}$. On RHS you get $(V_1-V_0) \frac{1-r^{n+1}}{1-r}$. The rest is simple algebra+boundary conditions (which you didn't provide). Can you handle from here?  
