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Young wolf
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Homework Statement
What is the remainder when (1*1!+2*2!+...+12*12!) Is divided by 13? Please give the answer along with the steps.
We cannot give the answer. We give hints, to solve the problem by yourself.Young wolf said:Homework Statement
What is the remainder when (1*1!+2*2!+...+12*12!) Is divided by 13? Please give the answer along with the steps.
Homework Equations
The Attempt at a Solution
The formula for calculating remainders is:
Remainder = Dividend % Divisor
Where % is the modulus operator, Dividend is the number being divided, and Divisor is the number the dividend is being divided by.
To solve this equation, first calculate the factorial of each number up to 12. Then, multiply each number by its corresponding factorial and add them all together. Finally, divide the sum by 13 and find the remainder using the formula mentioned above.
The use of factorials in this equation is significant because it represents the number of ways to arrange a set of objects in a particular order. In this case, the numbers 1 to 12 are being arranged in different orders, and the factorials account for those different arrangements.
Yes, this equation can be solved without using factorials. However, using factorials makes it easier to understand and calculate the solution.
The solution to this equation is a remainder of 2. This means that when the sum of (1*1!+2*2!+...+12*12!) is divided by 13, the remainder is 2.