Sequence of sequences/Sum sequence with growing number of summands/Exercise

Suppose that for every natural number $k$, a null sequence $y_k$ is given, we denote the $n$-th member of the $k$-th sequence by $y_{kn}$. Is the sequence $z_n$, whose $n$-th member is defined by

$z_n=\sum _{k=1}^n{y}_{kn},$

also a null sequence?

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