We must solve these exercises using MATLAB . Create a vector u with the elements

Question

We must solve these exercises using MATLAB.

Create a vector u with the elements, u_n = (-1)^n+1/2n - 1, Forall n greaterthanorequalto 1 Write a program to compute the terms of the sequence given by: z_2 = 2, z_n+1 = 2^n-1/2 squareroot 1 - squareroot 1 - (4^1-n) z^2_n = 2, 3.... Compare the numerical result with the exact limit: lim_n rightarrow infinity z_n = pi. Create a stoping criterion that stops the program after achieving an accuracy of order 5. Given two matrices A = (a_i, j) Element M_n, p and B = (b_i j) Element M_n p, program a script that compute the Hadamar product A compositefunction B = (a_i j b_i j). As pi is the sum of the series pi = sigma^infinity _n=0 16^-n (4/8n + 1 - 2/8n + 4 - 1/8n + 5 - 1/8n + 6), we can compute an approximation of pi by summing up the n first terms for n large. Write a Matlab program that compute the partial sums of this series. For which value of n, we obtain an approximation of pi of order 10^-6. Write a Matlab program that compute the binomial coefficients C^k_n = n!/k!(n - k)!

Explanation / Answer

Exersise 1:

n = input('Enter n: ');
u = rand(n, 1)

for i = 1:n
    u(i) = (-1)^(i+2)/(2*i - 1);
end
u

Buddy we are suppose to solve one 1 question at a time with maximum 4 subparts. I would request you to re post questions seperatly. I hope you understand and co-operate.

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