Question

Calculate ? using the approximation n! n ! is the factorial: n!-1 × 2 × 3 × × n. |1×3 x-..×n, nis odd n!! is the semifactorial: n!!-12 x 4 x x n, n is even not to be confused with (n!)!, which is the factorial function iterated twice. The semifactorial of n is the product of the integers between 1 and n which have the same parity (even or odd) as n. For example, 7!! 1 × 3 × 5 × 7 = 105, and 8!! 2 x 4 x 6 x 8-384. MATLAB has a built-in factorial function, but you are required to write the semifactorial function yourself. The sum given above goes to infinity. Your MATLAB function should take a single input argument which specifies how many terms of the summation should be computed.

Answer 1

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Output

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disp('Input n')

n = input()

res = 0;

% calculate the product

for k= 1:n

f =(factorial1(k)/factorial2(2*k+1));

res = res+f;

end

res = 2*(1+res)

function fact = factorial1(num1)

fact = 1;

% calculate the factrial of num1

for i= 1:num1

fact = fact* i;

end

end

function fact1 = factorial2(num2)

fact1 = 1;

j=num2;

k=num2;

%calculate semifactorial of num2

for i= 1:ceil(num2/2)

% if num2 is even then compute 4*2..

if mod(num2,2)==0

fact1 = fact1*j;

j = j-2;

else

% fi num2 is odd then compute 7*5*3*1..

fact1 = fact1*k;

k = k-2;

end

end

end

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