Find the sum of series for which n-th term is given by an= 4/(5^n)
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- Find the order of growth for the following function ((n^3) − (60n^2) − 5)(nlog(n) + 3^n )Show that StartFraction d Over dx EndFraction (ln kx)equalsStartFraction d Over dx EndFraction ln x, given that xgreater than 0 and kgreater than 0 is a real number.Given an array A of n distinct positive integers and an integer B, find the number of unordered pairs of indices(i and j) such that i != j and that A[i] + A[j] > B using an algorithim in time nlogn. Prove that the algorithm you have is in time nlogn
- Generate the graph of f(xk) vs k where k is the iteration number and xk is the current estimate of x at iteration k. This graph should convey the decreasing nature of function values.Solve this recurrence relations together with the initialconditions given. a_{n+2} = −4a_{n+1} + 5a_n for n ≥ 0, a_0 = 2, a_1 = 8find the adjacent matrix not the adjacent list