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

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Omar B. on 23 Jul 2021
Commented: Omar B. on 23 Jul 2021
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)+...
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Omar B. on 23 Jul 2021
I could not find the formula. I want a double precision answer.

Debarati Bhattacharyya on 23 Jul 2021
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. on 23 Jul 2021
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);

dpb on 23 Jul 2021
Edited: dpb on 23 Jul 2021
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. on 23 Jul 2021
Thank you so much.