Final answer:
The statement that the sum of EPSPs can cause a neuron to reach the threshold and generate an action potential is true, as multiple EPSPs usually sum together to surpass the required membrane potential threshold.
Step-by-step explanation:
If the sum of the excitatory postsynaptic potentials (EPSPs) causes a postsynaptic neuron to reach its threshold, then the postsynaptic neuron will generate an action potential. This statement is True. An EPSP is a depolarizing event that increases the likelihood that a neuron will fire an action potential. However, it often takes the summation of multiple EPSPs, occurring close in time and space, to push the neuron's membrane potential to the threshold required for triggering an action potential. Furthermore, inhibitory postsynaptic potentials (IPSPs) can counterbalance EPSPs, and only the net change in membrane potential decides if the threshold will be reached. Therefore, not just random potentials but a concerted and sufficient shift in these potentials will lead to an action potential.