Question

11. (20 points) A beautiful formula relating the irrational number 1, and the integers is the following thus, one can approximate ~ En 1 with N being a finite number. Write an matlab function that computes the value of inis sum for a given input parameter N. Use this function within a main program to plot y(N)= m vs. N, with N ranging from 1 to 1000.

Answer 1

function y = sumN(n)

sum=0;

for i=1:n

sum += (1/(i*i));

end

y=sum;   
end

1 A function y = SUMN(n) 2 SUM=; 3 for 1-1:n sum += (1/(i*i); end y=sum; end

save this code as sumN.m

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sums = linspace(1,1000,1000);

for N = 1:1000

sums(N) = sumN(N);
end

plot(sums)

xlabel("N");

ylabel("y");   

2 3 sums = linspace(1, 1000, 1000); for N = 1:1000 SUMS(N) = SUMN(N); end L 5 6 7 8 9 plot(sums) xlabel(""); ylabel("");

output is:--

200 00 400 N 600 800 1000

P.S.-> just for observation:- y value for N=1000 is 1.6439. and pi*pi/6 is 1.6449 so as can be seen larger value for N is approaching pi*pi/6 value as the graph is seen increasing slowly..

thanks