Develop an iterative $($non$-$recursive$)$ time and space$-$efficient algorithm to determine the sum of the

following series $($for inputs X and n$)$: $1+$ X $+$ X$^2+$ X$^3+...+$ Xn such that the number of

multiplications encountered is a linear function of $\text{'}$n$\text{'}($i$.$e$.,$ of the order of $\text{'}$n$\text{'}).$

$($i$)$ Determine the basic operation of your algorithm.

$($ii$)$ Is there a best case different from worst case or the best case is same as the worst case? Justify your

answer with an explanation as well as an example.

$($iii$)$ Depending on your answer for $($ii$),$ determine the best case as well as the worst case $($if the best case

is different from worst case$)$ or just the number of times $($if the best case is the same as the worst case$)$ the

basic operation is executed as a function of the input size $\text{'}$n$\text{'}.$ Justify your answer.

$($iv$)$ Is your algorithm in$-$place or not with respect to space complexity? Justify your answer.