how to write a Matlab code to sum 10 terms of rational numbers?

How to write a matlab code to find the sum of 10 terms of the follwing series:

(39/2)-(36/5)+(31/10)-(24/17)+...

[James Tursa]

What is the formula for the terms? Do you want a double precision answer, or an exact fraction (i.e. symbolic) answer?

[Omar B.]

I could not find the formula. I want a double precision answer.

Answer 1

[Debarati Bhattacharyya]

Hi Omar,

Please find the function below which calculates the sum of the series as you are looking for:

function calculateSum(num_of_terms)

% To calculate the sum of the below series upto n terms

% 'n' is provided by the user

% (39/2)-(36/5)+(31/10)-(24/17)+...

sum = 0;

first_num = 39;

first_denom = 2;

for k = 1:num_of_terms

disp([num2str(first_num), '/', num2str(first_denom)]);

sum = sum + (-1)^(k+1)*((first_num)/(first_denom));

first_num = (first_num-(2*k+1));

first_denom = (first_denom+(2*k+1));

end

disp(sum);

end

Please let me know if this works for you!

[Omar B.]

Thank you so much.

I also tried

sum=0;
for k=1:10
  sum = sum + (-1)^(k-1)*((40-k^2)/(k^2+1));    
    end
>> disp(sum);

Answer 2

[dpb]

N1=39; d1=8;
N2=36; d2=12;
D1=2; D2=5;
S=N1/D1-N2/D2;
for i=2:10
  N1=N1-d1;
  N2=N2-d2;
  D1=D1+d1;
  D2=D2+d2
  S=S+N1/D1-N2/D2;
end

It could be written with vectors and colon more concisely; above is "dead-ahead" brute approach...

[Omar B.]

Thank you so much.