Question

Anyone can help? Thanks!

Question 1. [5 pts) In the following problems, a, b and c are positive constants, In n stands for the natural logarithm of n. a) True or false: If f(n) = an + bnº.5, then f(n) = O(n). b) True or false: If f(n) = ans + bn + c, then f(n) = 0 (n?). c) True or false: If f(n) = an', then f(n) = N(Inn). d) Let f(n) = $1=1 give a Big- notation for f(n) (i.e. find some function g(n) such that f(n) = (g(n))). e) Let f(n) = x=1 i 2, give a Big-notation for f(n).

Answer 1

$\small \color{blue}Answer:\;\;$

a)  True
b)  True
c)  True
d)  ?(ln n)
because sum of all terms in harmonic series is <= lg(n)
e)  ?(n^3)
because sum of squares of n numbers is n(n+1)(2n+1)/6
after ignoring constant terms we get n^3