Use MATLAB to solve each problem. Some of the commands you may need on this assi

Question

Use MATLAB to solve each problem. Some of the commands you may need on this assignment are: syms, limit, symsum, factorial, and double. Note: If you define a sequence in MATLAB using the form a(n) -..., then running the command a(1:5) will return the first five terms of the sequence. 1. (3 points) For each of the following sequences, (I) Find the first 10 terms of the sequence. (II) Determine if the sequence converges or diverges , n21 a) an- (b) an - (2n)5/n, n 2 1 C) an- T2 n! (d)2n)! 4n - 3 2n+1 (e) an-(4n+5 n> 1

Explanation / Answer

%a(n) convergence series
% n=inf
% e = 1+3/inf = 1+0 = 1
%a(inf)= 1^(4*inf) = 1^inf = 1
% if a(n) == finite value function is convergence
for n = 1:10;
e = 1+3/n;
a(n) = e^(4*n);
end
sprintf('%.2f ',a)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%a(n)Divergence series
% n=inf
% e = 2*inf = inf
%a(inf)=inf^(4*inf) = inf^inf = inf
% if a(n) lim n->inf != 0 or finite value, function is divergence
for n = 1:10;
e = 2*n;
a(n) = e^(5/n);
end
sprintf('%.2f ',a)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%a(n)convergence series
% n=inf
% e = inf*(-inf) = 0
%a(inf)=0/n! = 0
% if a(n) lim n->inf == 0 function is convergence
for n = 1:10;
e = n^(-n);
a(n) = e/(factorial(n));
end
sprintf('%.2f ',a)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

%a(n)convergence series
% n=inf
% e = factorial(inf) = inf
%a(inf)= 2*e/e = 2
% if a(n) lim n->inf == constnt finite value, function is convergence
for n = 1:10;
e = factorial(n);
a(n) = 2*e/e;
end
sprintf('%.2f ',a)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%a(n)Divergence series
% n=inf
% e = 4*inf - 3 = inf
% f = 4*inf + 5 = inf
%a(inf)= (e/f)^(2*inf+1) = (1)^inf = 1
% if a(n) lim n->inf == finite value, function is convergence
for n = 1:10;
e = 4*n-3;
f = 4*n+5
a(n) = (e/f)^(2*n+1);
end
sprintf('%.2f ',a)

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