This question is written in MATLAB Given an integer N, it is required to compute

Question

This question is written in MATLAB

Given an integer N, it is required to compute the sum of the numbers from I to N. The sum can be computed directly or analytically by the following formula: S = 1+2+3+ +N = 1/2 N (N + 1) Let N = 20. Compute the sum by the following 5 methods, using: (1) a for-loop, (2) a conventional while-loop, (3) a forever while-loop, (4) the vectorized sum function, and, (5) the above analytical formula Write a function, say, fsum.m, that employs a switch structure and evaluates the sum by any of the above 5 methods, with method 5 being the default method. It must have the following usage, where m is the method number, m = 1, 2, 3, 4, 5: S = fsum(N, m) The sum S grows with increasing N. Using your function fsum and a forever while loop determine the smallest N such that S > 10^6. Repeat using a conventional while-loop. Do not use the built-in functions sum or cumsum in this problem. Write your code and numerical results for parts (a, b, c) in the space below.

Explanation / Answer

(a) The answer is 210.

1)

n=20;

sum1=0;

for i = 1:n
sum1 += i;
end

disp(sum1);

2)

n=20;

sum1=0;

while(i<=n)
sum1 += i;
i+=1;
end

disp(sum1);

3)

n=20;

sum1=0;

while 1
sum1 += i;
i+=1;
if(i>n)
break
end
end

disp(sum1);

4)

n=20;

arr = 1:n;
sum1 = sum(arr);   

disp(sum1);

5)

n=20

sum1 = (n*(n+1))/2;

disp(sum1);

(b)

function sum1 = fsum(n,m)
sum1 =0;
switch(m)
case 1
for i = 1:n
sum1 += i;
end
case 2
i=0;
while(i<=n)
sum1 += i;
i+=1;
end
case 3
i=0;
while 1
sum1 += i;
i+=1;
if(i>n)
break
end
end
case 4
arr = 1:n;
sum1 = sum(arr);
case 5
sum1 = (n*(n+1))/2;
otherwise
sum1 = (n*(n+1))/2;
end
end
disp(fsum(100,1));
disp(fsum(100,2));
disp(fsum(100,3));
disp(fsum(100,4));
disp(fsum(100,5));
disp(fsum(100,6));

(c) The answer is 1414

Forever while loop:

st = 1;
while 1
if(fsum(st,5)>1000000)
break;
end
st+=1;
end
disp(st);

traditional while loop:

st = 1;
while(fsum(st,5)<1000000)
st+=1;
end
disp(st);

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