Can you use the sum formula for a geometric series starting at any point?

sequences-and-series

\begin{align*} ar^{100} + ar^{101} + ar^{102} + \text{ ... } &= r^{100}\big[a + ar + ar^{2} + \text{ ... } \big] \\ &= \dfrac{ar^{100}}{1-r} \end{align*} So factoring out $r^{100}$, yes you have the same form.

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