When an electric signal reaches a chemical synapse, the signal is transmitted using neurotransmitters. Afterwards, the neurotransmitters are removed from the synaptic cleft. My question is whether it happens in a normally functioning brain that neurotransmitter concentrations in the synaptic cleft add up if there are several impulses in quick succession? If so, does this serve any purpose? Or is the time between two impulses always long enough for all of the neurotransmitter to be removed from the synaptic cleft?
Edit: To further clarify (as the currently only answer does not really adress my issue), I am aware of the principle of summation, however I do not know whether this is actually caused by multiple neurotransmitter emissions "adding up" in the synaptic cleft or whether the postsynaptic membrane can just somehow remember if there was an increased amount of neurotransmitter recently.
To describe it graphically: According to this article, the concentration of serotonin in the synaptic cleft during a single impulse looks somewhat like that. Now when there is a quick series of impulses, does the neurotransmitter always get removed before the next impulse as on the right side of the following image, or can it add up as on the left side? And if it does add up, does this actually serve the purpose of temporal summation or some other purpose?