To expand  (a + b)n,  we can use the       Theorem. Using this theorem, we find the expansion  (a + b)4 =         a4 +         a3b +         a2b2 +         ab3 +         b4.

TRUE OR FALSE N Queens' problem can be effectively solved using dynamic programming.

Solve the recurrence by using repeated substitution. Show the work.   T(n) = T(n-1) + n

Show that 5n+5 is O(n). (pick c and n0)

Please solve using iterative method: Solve the following recurrences and compute the asymptotic upper bounds. Assume that T(n) is a constant for sufficiently small n. Make your bounds as tight as possible. a. T(n) = T(n − 2) + √n b.T(n) = 2T(n − 1) + c

2) Prove divisible by 3 for any integer nzo. that n(n²+s) is divisible by 3 for Let n 1 1 (1² +5) = 1(1+5)=(6/ K(K²+5) K+ 1 ((k + 1 ) ² + 5

Use induction to show that 4n < 2nfor all n ≥5

To expand  (a + b)n,  we can use the       Theorem. Using this theorem, we find the expansion  (a + b)4 =          a4 +          a3b +          a2b2 +          ab3 +          b

Give asymptotic upper and lower bounds for each of the following recurrences. Justify your answer.

7. Prove that if 7 divides n with remainder 1, 7 divides n² + 2n +7 with remainder 3.