Transcribed Text
1. (5 pts) Compute the following sums. You do not have to fully simplify your answer but your answer
cannot have a summation (symbol) in it.
(a)
18
1
i3
(b)
[2f
(c)
(2i4)
2. (4 pts) Prove that
((2i4)EO(nf)
1
3. (2 pts) Let f(n)  n2, g(n)  n h(n) n° and p(ni)  n. For each statement, fill in the blank with the
best answer from f(n), g(n), h(n) or p(n), that fits the statement.
a)3n³ log 115n+2e O(
b)7n4 n logn+
)
4. (5 pts) Consider the following pseudocode. How many times is the print subroutine called? Write your
answer first using sums and then compute the closed form it (e.g., the closed form of

i is n(n +1)/2).
i1
Assume that nis large enough for both loops to execute at least once.
for from 1 to n do
for from 2 ton*n do
print 'Q'
end do
print newline
end do
5. (4 pts) Prove that / (n)  3n³4n² +17 e (2(n)). Show your work.
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