)The formula for solving this problem is: ∑(k=100)^200 k^3 = (200^2 * (200+1)^2) / 4 - (99^2 * (99+1)^2) / 4.
To solve this problem, you can use the formula for the sum of consecutive cubes: ∑(k=1)^n k^3 = (n^2 * (n+1)^2) / 4. You can then plug in the values for n=200 and n=99 and subtract the two values to get the final answer.
Yes, it is possible to solve this problem without using a formula. One approach is to break down the sum into smaller, more manageable parts. For example, you can group the terms into (100^3 + 101^3 + 102^3) + (103^3 + 104^3 + 105^3) + ... + (199^3 + 200^3). From there, you can use basic arithmetic to find the sum of each group and then add them together to get the final answer.
Yes, this type of problem can be found in various fields such as mathematics, physics, and engineering. For example, calculating the sum of consecutive cubes can be used in physics to determine the total work done by a variable force over a certain distance.
Sure, let's say you want to calculate the total cost of renting a car for a certain number of days. The daily rental rate is $50, and you want to rent the car for 10 days. Using the formula for the sum of consecutive cubes, you can find the total cost as follows: ∑(k=1)^10 50k = (10^2 * (10+1)^2) / 4 = $2,750. So, the total cost of renting the car for 10 days would be $2,750.