Question 1: Find the sum S of the series where S = S iai– here i varies from 1 to n.
Question 2: S = S 2n-i i2 here, i varies from 1 to n. Show that sum S is O(n22n).
Question 3: Show that 9(9n -1) – 8n is divisible by 64. Use induction.
Show all the steps and calculations for each of the above and explain your answer in detail.