Question

Part B: In mathematics a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus. Write matlab code that calculates and displays the sum of the values of the series 5k^2-2k where we only have 15 values of k (k=1,2,3...15). Use a for loop . Be sure to initialize the total at the very beginning of your code. The total should be 5960

PartC: Write a matlab program ( using a while loop) to determine the number of terms ( which we’ll call s) required for the sum of the series in part B to exceed ten thousand. Display the number of terms. The answer should be 18

Answer 1

%% Matlab code to calculate the sum of the series
%
sum=0; % initilalizing the sum value with '0'
for k=1:1:15 % find the sum of series for k= 1 to 15
S=5*k^2-2*k; % expression of the series, for k
sum=sum+S; % adding the value of series at k to the previous sum
end % end of the for loop
sum=sum

%% Matlab code to find the number of numbers to be in series, so that
% the sum is greater than a value
%
sum=0; % initializing the sum value with '0'
k=0;
while sum<10000 % checkk wether the sum is exceeding 10000, if not it
% will continue to add the next number
k=k+1; % if the sum doesnt exceed 10000, then k will increase
% to next number
S=5*k^2-2*k; % expression of the series, for k
sum=sum+S; % adding the value of series at k to the previous sum
  
end % end of the while loop. exits when sum exceeds 10000
k=k
% now the k value will be the number of terms required for the sum of
% the series is exceeds ten thousand