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Consider the equality $\sum_{i=1}^{n} f(i) = n^2 + 2n$, where $f(i)$ is some function of the iterator $i$.

For which of the following does the equality hold?

$i^2 + 2i$

$(2i - 1)^2$

$(i+1)^2 - i^2$

$i(2i - 1)$

$i(i+1)^2$