Final answer:
To simplify the sum 4∑i=0j20i, we can factor out 20 and use the formula for the sum of numbers from 0 to j. The final simplified expression is 40(j(j+1)).
Step-by-step explanation:
To simplify the sum 4∑i=0j20i, we need to understand the notation. ∑ is the summation symbol, j is the upper limit of the summation, and i=0 is the lower limit. In this case, we are summing 20i for each value of i from 0 to j. So, we can rewrite the expression as 4(20(0)+20(1)+20(2)+...+20(j)).
To simplify the expression further, we can factor out 20 from each term: 4(20(0+1+2+...+j)). The sum of the numbers from 0 to j is given by the formula (j(j+1))/2. So, the simplified expression is 4(20(j(j+1))/2).
Finally, we can simplify the expression even further by canceling out 2 from the numerator with 4 in the denominator, resulting in 40(j(j+1)). This is the simplified form of the given sum.