Develop a time and space-efficient algorithm to determine the sum of the following series (for inputs X and n): 1+X+X + X + ... + X" such that the number of multiplications encountered is a linear function of 'n' (i.e., of the order of 'n'). (i - 3 pts) Determine the basic operation of your algorithm. (ii - 7 pts) 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 - 7 pts) 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 'n'. Justify your answer. (iv - 3 pts) Is your algorithm in-place or not with respect to space complexity? Justify your