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Part $3$$\newline$The sum of a finite of a geometric series can be found by$\newline$$$S_n = \frac{a_1(1-r^n)}{1-r}$$$\newline$Derive the formula for the sum of a finite geometric series.$\newline$[Hint:$\newline$a) Start with the general geometric series$\newline$$$S_n = a_1 + a_1r + a_1r^2 + a_1r^3 + \dots + a_1r^{n-1}$$$\newline$with common ratio $\newline$$$r$$$\newline$b) Multiply both sides of this equation by $\newline$$$-r$$.$\newline$c) Add the results of $\newline$a. and $\newline$b. and then do some algebraic rearranging.]$\newline$$11$. Find $\newline$$$S_{10}$$ for the geometric series with $\newline$$$a_1=5$$ and $\newline$$$r=3$$$\newline$$166$