Sequence and Series: JEE Main 2023 Mathematics question

For $k \in \mathbb{N}$, if the sum of the series $1+\frac{4}{k}+\frac{8}{k^{2}}+\frac{13}{k^{3}}+\frac{19}{k^{4}}+\ldots$ is 10 , then the value of $k$ is _________.