# The system y[n] = $∑_{k=-∞}^n x[k]$ is an example of ____________

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The system y[n] = $∑_{k=-∞}^n x[k]$  is an example of ____________

(a) Invertible system

(b) Memoryless system

(c) Non-invertible system

(d) Averaging system

This question was addressed to me in an online quiz.

This key question is from Characterization and Nature of Systems in division Laplace Transform and System Design of Signals and Systems

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The correct choice is (a) Invertible system

To explain I would say: Given that, y[n] = $∑_{k=-∞}^n x[k]$

We know that if a system is invertible, then an inverse system exists that, when cascaded with the original system, yields an output w[n] equal to the input x[n] to the first system.

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