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Find the order of growth of the following sums. Use the Theta ( notation with the simplest function g ( n ) possible. (

Find the order of growth of the following sums. Use the \Theta (notation with the
simplest function g(n) possible.(5 points) Write an algorithm variation of sequential search that scans a list to return the number of
occurrences of a given search key in the list. Does its efficiency differ from the efficiency of classic
sequential search?
(5 points) Suggest how any sorting algorithm can be augmented in a way to make the best-case
count of its key comparisons equal to just n-1(n is a list's size, of course). Do you think it would
be a worthwhile addition to any sorting algorithm?
(5 points) For each of the following pairs of functions, indicate whether the first function of each of
the following pairs has a lower, same, or higher order of growth (to within a constant multiple)
than the second function. Use ({:,:)1==
a.n(n+1),2000n2
b.n2,n3
c.logn,lnn
d.(n-1)!,2n
(5 points) Compute the following sums.
a.1+3+5+7+dots+999
b.i=1n+1i
c.i=0n-1i(i+1)
d.i=1nj=1nij
(5 points) Find the order of growth of the following sums. Use the (g(n)) notation with the
simplest function g(n) possible.
a.t=0n-1(i2+1)2
b.t=2n-1logt2
c.i=1n(i+1)2i-1
d.t=0n-1j=0i-1(i+j)
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