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Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be?
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Let p, be a natural number from 1 to 99. Then the product of all the f...
Understanding the Problem
To solve the problem, we need to analyze the product of fractions of the form P/(p+1), where p is a natural number ranging from 1 to 99.
Form of the Fractions
- Each fraction can be represented as:
- P/2, P/3, P/4, ..., P/100
- This means we will have a total of 99 fractions, corresponding to each natural number p from 1 to 99.
Calculating the Product
- The product of these fractions can be expressed as:
- (P/2) * (P/3) * (P/4) * ... * (P/100)
Factoring Out P
- We can factor out P from each term:
- P^99 / (2 * 3 * 4 * ... * 100)
Understanding the Denominator
- The denominator, 2 * 3 * 4 * ... * 100, is essentially the factorial of 100 divided by 1:
- This can be denoted as 100! / 1
- Hence, the complete product can be summarized as:
- P^99 / 100!
Conclusion
- The product of all the fractions of the form P/(p+1) for p from 1 to 99 will yield:
- P^99 / 100!
- This expression neatly encapsulates the relationship between P and the factorial of the upper limit of our range.
This clearly outlines how to approach and solve the problem while emphasizing the mathematical relationships involved.
To solve the problem, we need to analyze the product of fractions of the form P/(p+1), where p is a natural number ranging from 1 to 99.
Form of the Fractions
- Each fraction can be represented as:
- P/2, P/3, P/4, ..., P/100
- This means we will have a total of 99 fractions, corresponding to each natural number p from 1 to 99.
Calculating the Product
- The product of these fractions can be expressed as:
- (P/2) * (P/3) * (P/4) * ... * (P/100)
Factoring Out P
- We can factor out P from each term:
- P^99 / (2 * 3 * 4 * ... * 100)
Understanding the Denominator
- The denominator, 2 * 3 * 4 * ... * 100, is essentially the factorial of 100 divided by 1:
- This can be denoted as 100! / 1
- Hence, the complete product can be summarized as:
- P^99 / 100!
Conclusion
- The product of all the fractions of the form P/(p+1) for p from 1 to 99 will yield:
- P^99 / 100!
- This expression neatly encapsulates the relationship between P and the factorial of the upper limit of our range.
This clearly outlines how to approach and solve the problem while emphasizing the mathematical relationships involved.
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Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be?
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Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be?.
Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will be?.
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