series RL analysis using Laplace

Hi Guys,

Could anyone offer some assistance please?(Thinking)

I have a question which states the following:

L[v(t)] = V(s) = 1/(1+s^s)(1-e^(pi*s)

if an inductor (1 H) and a resistor (1 Ohm) are connected in series then show that the resulting current is,

**i(t)=sigma(n=0,infinity).f(t-n*pi)**

where f(t) =(sin(t)-cos(t)+e^(-t))u(t)

i am able to analysis the circuit to give the following:

L[di/dt] +L[Ri]=L[v(t)] giving I(s)=1/(s+1)(s^2+1)(1-e^(pi*s))

using partial fractions it becomes:

I(s)=(1/(1-e^(-pi*s)))*0.5*((-s/(s^2+1))+(1/(s^2+1))+(1/(s+1))

I am really not sure where to go next, I am sure that 1/(1-e^(-s*pi)) is some kind of geometric series but other than that I am stumped!

I would really appreciate it if someone could point me in the right direction.

Regards,

Mckiseldeck