Find the interval of convergence for Ž (-1)" (2x+1)" 0 3n+1
8. Use induction (on n) to show that: (a) (2n)! > 2" (n!)?, for n > 0. (w) (%) = (2+1), for os ms m. (0) Ž -»* (*) = (–1"("m"), for os m<n.
n=í (2n)! 2 ants (d) 0 2 ant} of these > #6 (18 pes) Find the Maclarin series of f1z)= 2²cos(22). (a) Ž L 22nt3 (-0, 3n+2 (5) não (2n)! (c) 2 nii (intl)! n! le) none #7 (15 pts) Find the Laurent series for 2444 in the region: 4<lz-zilco (5) Ź (2-zinte não lz-right2, (2i)" não 17-2i) 2, Cal 922–25" le) none of these hao la) (40) (c) Ř (Ztri)? no
Multiply and simplify. (3n)2 (3n) 8
Solve the difference equationy(n + 2) + 4y(n + 1) +3y(n) = 3n with y(0) =0, y(1) = 1
-) f(n)=n+1 g(n) = 3n² – 3 Find (fºg)(8)
Prove the following: 1+4+7+...+(3n – 2) n(3n-1) 2
Use the pumping lemma to show that the following languages are not context free: a)0^n0^2n0^3n;n>=0 b) {w#x \ where w.x e {a,b) * and w is a substring of x} c) (a^ib^ja^ib^j|i,j>0) answer should be very clear .otherwise I will down vote .
Use the equation 1 1x = Ž for 1x1 <1 1 - X n = 0 to expand the function in a power series with center c = 0. 1 f(x) 5 + x3 00 Σ n = 0 Determine the interval of convergence. (Enter your answer using interval otation.)
The solution to the Traveling Salesperson Problem using Exhaustive Search is 0 (_ _) ? Ž Z Z The worst case brute force time complexity of searching for a pattern of length Min a text of length Nis O(NM) 0(N+M)! O(NM) O(N + M)