Hi Chithralekha,
The two pieces of code are not equivalent, and that is why they are producing different results. In first piece of code, the value of s(i) is being calculated for each i from 1 to 20, and then summed up the current value of s(i) in each iteration. This means s1 will only hold the value of the last element s(20) because it is being overwritten in each iteration.
In the second piece of code, s is initialized to 0 at each iteration of k, then sum is calculated for the value of 2 * acf(j+1)^2 from j=1 to j=k. The final value of s will be the sum of all these values up to k=20.
Hope this helps!
