Final answer:
The student seeks to calculate the output of an LTI discrete system, given the impulse response and a cosine input. The exact convolution computation cannot be completed without additional information or assumptions.
Step-by-step explanation:
The student is asking how to compute the output of a LTI discrete system with an impulse response h[n] = (21/n)u[n] when the input is x[n] = cos(4πn/2). An LTI (Linear Time-Invariant) system's output can be found by convolving the input signal with the system's impulse response. In this case, the frequency of the cosine input signal is such that it simplifies to cos(πn), which is an alternating sequence of 1 and -1. However, since the problem statement appears to be incomplete and not all necessary details are provided, the exact convolution operation cannot be fully described without the assumption of non-standard conventions or additional information.