1. Prove or disprove that xⁿ is not equal to O((log_e x)ⁿ) for any integer n>=1, where x > 1.

2. Let X = {x₁, x₂, x₃ , ....., x_n} be a sequence of arbitrary numbers (positive, zero, or negative). Give an O(n) time algorithm to find the subsequence of consecutive elements x_i, x_i+1,....,x_j whose sum is maximum over all consecutive subsequences. For example, for X = {2,5 ,-10, 3,12,-2,10,-7,5}, {3,12,-2,10} is a solution