- #1
kathrynag
- 598
- 0
Homework Statement
I'm trying to prove k*(k!)=(k+1)!-1
Homework Equations
The Attempt at a Solution
This is how far I've gotten:
k[k(k-1)(k-2)...1)]
mutton said:Are you sure the question doesn't say k * k! = (k + 1)! - k!?
kathrynag said:Well it's 1*1!+2*2!+...+k*k!=(k + 1)! - k!
kathrynag said:Well it's 1*1!+2*2!+...+k*k!=(k + 1)! - k!
kathrynag said:1*1!+2*2!+...+k*k!=(k + 1)! - 1
sorry...
Factorial simplifying is a mathematical process of simplifying expressions containing factorial notation. Factorial notation is denoted by an exclamation mark (!) and represents the product of all positive integers less than or equal to the given number.
Factorial simplifying is useful in many areas of mathematics, such as combinatorics, probability, and calculus. It allows for simpler and more efficient calculations and can help identify patterns in complex expressions.
The basic rules of factorial simplifying include the product rule (n! * m! = (n+m)!), the quotient rule (n! / m! = (n-m)!), and the power rule ((n!)^m = n! * (n-1)! * (n-2)! * ... * (n-m+1)!).
No, factorial simplifying can only be applied to expressions containing factorial notation. It is not applicable to other types of mathematical notation, such as exponential or logarithmic notation.
Yes, some common mistakes to avoid when simplifying factorials include incorrectly expanding or canceling out terms, forgetting to include the necessary factors in the final answer, and using the wrong rules for simplifying. It is important to double-check all steps and follow the rules carefully to avoid errors.