a) For all 6 methods, write out a formula to represent the growth rate of the method and reduce the formula to big-o notation.

Summation One: sum = 0; for(i = 0; i < n; i++) sum++;

Summation Two: sum = 0; for(i = 0; i < n; i++) for(j = 0; j < n; j++) sum++;

Summation Three: sum = 0; for(i = 0; i < n; i++) for(j = 0; j < n*n; j++) sum++;

Summation Four: sum = 0; for(i = 0; i < n; i++) for(j = 0; j < i; j++) sum++;

Summation Five: sum = 0; for(i = 0; i < n; i++) for(j = 0; j < i*i j++) for(k = 0; k < j; k++) sum++;Summation Six: sum = 0; for(i = 1; j < n; i++) for(j = 1; j < i*i; j++) if(j%i == 0) for(k = 0; k < j; k++) sum++;