Simplifying formulas with factorials (2n-1)

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The discussion focuses on simplifying the factorial expression (2n+1)!. It clarifies that (2n+1)! is not the same as (2n-1)!, as (2n+1)! can be expressed as (2n+1)(2n)(2n-1)!. The simplification shows the relationship between the two factorials. The conclusion emphasizes that (2n+1)! cannot be reduced to (2n-1)!. Understanding these factorial relationships is crucial for simplifying complex mathematical expressions.
wallz
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How would you simplify (2n+1)!
Is the same as (2n-1)! ?
 
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wallz said:
How would you simplify (2n+1)!
That's about as simple is it can be made.
wallz said:
Is the same as (2n-1)! ?
No, since (2n + 1)! = (2n + 1)(2n)(2n - 1)!
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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