I need to apply Laplace transform on this signal
and i'm just stuck with this one so can anybody please help me with this
any help will be most appreciated
What is T? Is is positive? If so, you can lose the Heaviside step function (it'll just be 1 everywhere). What do you have on the LHS of this equation? Finally, assuming you can ignore the step function, you can rewrite the sum this way:
Does that suggest anything to you?
It's true that the sequence probably converges to zero. But that doesn't mean the series
converges to zero.