Use MATLAB to show that the sum of the infinite series (12)* (sigma from n=0 to N) (3)^(n)/(2*n+1)

is equal to as N . Do this by computing the sum for various values of N, entered by the user. The script should continue to ask the user to input another value of N until a 0 is entered. Then, the script will end. The program should also check that N is an integer greater than or equal to 0 and if it is not, ask the user to enter N again.

In terms of calculating the sum, perform the same calculations using element-by-element operations instead of what we had done in class previously using a loop. To start, create a vector n in which the first element is 0, the increment is 1 and the last term is N. Then use element-by-element operations to create a vector in which the elements are

sqrt(12) *((3)*^(n))/ (2*n+1)

Finally, use the function sum to add the terms of the series and multiply the result by Test your code using the values for N specified in parts (a), (b), and (c). How do these values compare to the value of in MATLAB? Use format long to see the variations in .

(a) N = 10 (b) N = 20 (c) N = 50