Class 7 Exam > Class 7 Questions > Let p, be a natural number from 1 to 99. Then...
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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
Only one correct answer
A. 98900 /999000
B. 1 /100
C.999 /9990
D. 99 /100?
Only one correct answer
A. 98900 /999000
B. 1 /100
C.999 /9990
D. 99 /100?
Most Upvoted Answer
Let p, be a natural number from 1 to 99. Then the product of all the f...
Understanding the Problem
To find the product of all fractions of the form P/(P+1) where P is a natural number from 1 to 99, we start by setting up the fractions:
- The fractions are: 1/2, 2/3, 3/4, ..., 99/100.
Calculating the Product
Let's denote the product as:
- Product = (1/2) * (2/3) * (3/4) * ... * (99/100)
Breaking Down the Product
Now, notice that in this product:
- The numerator of each fraction cancels with the denominator of the next fraction.
- This leads to a telescoping effect.
Resulting Expression
After cancellation, we are left with:
- Product = 1/100
Final Answer
Hence, the value of the product of all these fractions is:
- Answer: 1/100
Thus, the correct option is B. 1 / 100.
This solution demonstrates how fractions can simplify through cancellation, revealing a straightforward result despite appearing complex at first glance.
To find the product of all fractions of the form P/(P+1) where P is a natural number from 1 to 99, we start by setting up the fractions:
- The fractions are: 1/2, 2/3, 3/4, ..., 99/100.
Calculating the Product
Let's denote the product as:
- Product = (1/2) * (2/3) * (3/4) * ... * (99/100)
Breaking Down the Product
Now, notice that in this product:
- The numerator of each fraction cancels with the denominator of the next fraction.
- This leads to a telescoping effect.
Resulting Expression
After cancellation, we are left with:
- Product = 1/100
Final Answer
Hence, the value of the product of all these fractions is:
- Answer: 1/100
Thus, the correct option is B. 1 / 100.
This solution demonstrates how fractions can simplify through cancellation, revealing a straightforward result despite appearing complex at first glance.
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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 beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100?
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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 beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100? for Class 7 2024 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 beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100? covers all topics & solutions for Class 7 2024 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 beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100?.
Let p, be a natural number from 1 to 99. Then the product of all the fractions of the form P p+1 will beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100? for Class 7 2024 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 beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100? covers all topics & solutions for Class 7 2024 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 beOnly one correct answerA. 98900 /999000B. 1 /100C.999 /9990D. 99 /100?.
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