How can I fix my problems in this program using loops?

The actual question asks to write a program (Using a loop) that determines the expression

m
2|-| ((2n)^2)/((2n)^2)-1)  =  2(4/3*16/15*36/35....)
n=1
(above is an infinite product series symbol)

Run the program with m = 100, m = 100,000, and m = 1,0000,000. Compare the result with π. (Use format long.)

So far this is what I have come up with in MATLAB

clc

clear all

format long

n=1;

S=0;

m=input('Enter m')

for n=1:m

    S(1:m)=2*(((2*n)^2))/(((2*n)^2)-1)

end

m

pi

[dpb]

Where's the summation????

You'll need to accumulate into S each term inside the loop on n to do the sum via looping...the LHS should be a single term to add each pass not a vector.

[Raghavendra]

Yes that's right..

create a dummy variable then keep accumulating the results into it, finally do the summation. s= []; %Initialize the dummy variable for n=1:m S = 2*(((2*n)^2))/(((2*n)^2)-1); % do the calculation s= [s;S];% store the result end Sum_S = sum(s); %get the sum

Answer 1

[David Sanchez]

I think your equation has a mistake, since for n=1 it yields 0, and subsequently, the result is 0 for being a multiplication. The idea behind the series recursion is the following. Adapt it to your equation and make sure you write it rightly.

S = 1;  % I start in one to yield non-zero result.
m = input('Enter m:  ');  
for n = 1:m  
    S = S*( (2*n)^2 /((2*n)^2 -1 ) );
end