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Solve equation with for loop function

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Annique Coetzer
Annique Coetzer il 4 Ago 2022
Commentato: John D'Errico il 18 Giu 2023
DAETERMINE IF BOTH IDENTITIES ARE CORRET FOR N=100 USING THE FOR LOOP FUNCTION IN MATLAB
  3 Commenti
Torsten
Torsten il 4 Ago 2022
Now you know at least that both formulas are true -:)
syms k n
s1 = symsum(k^3,k,1,n)
s1 = 
s2 = symsum((-1)^(k+1)*k^2,k,1,n)
s2 = 
Walter Roberson
Walter Roberson il 4 Ago 2022
syms k n
s3 = symsum((-k)^5, k, 1, n)
s3 = 
subs(s3, n, 10)
ans = 
k = 1:10;
sum((-k).^5)
ans = -220825
Now, how could one write a summation as a for loop ?

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Risposte (1)

Shantanu Dixit
Shantanu Dixit il 18 Giu 2023
Hi Annique,
Verify both the identites using for loop (using n = 100) and the identity formula.
1.
n = 100;
sum_n_cubes = 0;
% Compute the sum of cubes using a for loop
for i = 1:n
sum_n_cubes = sum_n_cubes + i^3;
end
disp(['Sum of first ', num2str(n), ' cubes is: ', num2str(sum_n_cubes)]);
Sum of first 100 cubes is: 25502500
% Compute the sum of cubes using identity
sum_n_cubes_identity = (n*(n+1)/2)^2;
disp(['Sum of first ',num2str(n),' cubes with identity: ',num2str(sum_n_cubes_identity)]);
Sum of first 100 cubes with identity: 25502500
2.
n = 100;
sum_n_series = 0;
% Compute the sum of cubes using a for loop
for i = 1:n
sum_n_series = sum_n_series + (-1)^(i+1)*i^2;
end
disp(['Sum of series using for loop: ', num2str(sum_n_series)]);
Sum of series using for loop: -5050
% Compute the sum of cubes using identity
sum_n_series_identity = (-1/2)*((-1)^n)*(n*(n+1));
disp(['Sum of series using identity: ', num2str(sum_n_series_identity)]);
Sum of series using identity: -5050
  1 Commento
John D'Errico
John D'Errico il 18 Giu 2023
@Shantanu Dixit - please don't do homework assignments for students when they have made no effort to do anything themselves. This only teaches the student that there is always some sucker willing to do their work for them. This is not a lesson they should learn here, or anywhere.
It does not help the student, teaching them only to post another homework assignment with no effort.
It does not help the site, infact, it actively hurts the site, since it then teaches other students to post their questions too.

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