I want to know whether the following is periodic or not periodic I have a question about system properties of the following function whether it is periodic or aperiodic. 
With an insight, I'd determine the function is aperiodic since the unit-step term looks implying that jump discontinuities occur at odd number times but don't have a detailed solution in mathematical terms.
Many thanks in advance for your help.
$$f(t)=\sum_{n=-\infty}^{+\infty}e^{-(2t-n)}u(2t-n)$$

The function is periodic with period $1/2$ since you have
$$
f(t+1/2)=\sum_{n=-\infty}^\infty e^{-(2t-n+1)}u(2t-n+1)=f(t),
$$
as you can easily see by an index shift in the sum.
Hope this helps...
