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Consider a sesequence s whose nth term is defined as 1 3/n,where n=1,2,3.find the product of all consecutive terms of s starting from 4th term to 60th term?
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Consider a sesequence s whose nth term is defined as 1 3/n,where n=1,2...
Introduction:
The given sequence s is defined by the formula s_n = 1 * (3/n), where n = 1, 2, 3, ...

Finding the terms:
To find the terms of the sequence, we substitute the values of n into the formula. Let's calculate the first few terms:

s_1 = 1 * (3/1) = 3
s_2 = 1 * (3/2) = 1.5
s_3 = 1 * (3/3) = 1

Product of consecutive terms:
To find the product of consecutive terms from the 4th term to the 60th term, we need to calculate the product of s_4 * s_5 * s_6 * ... * s_60.

Let's calculate the product of the first few terms as an example:

s_4 = 1 * (3/4) = 0.75
s_5 = 1 * (3/5) = 0.6
s_6 = 1 * (3/6) = 0.5

Product of s_4 * s_5 * s_6 = 0.75 * 0.6 * 0.5 = 0.225

General formula for the nth term:
We can observe that the nth term of the sequence s can be written as s_n = 1 * (3/n) = 3/n.

Product of consecutive terms:
To find the product of consecutive terms from the 4th term to the 60th term, we can write it as:

s_4 * s_5 * s_6 * ... * s_60 = (3/4) * (3/5) * (3/6) * ... * (3/60)

We can cancel out the common factors of 3 in the numerator and denominator:

(3/4) * (3/5) * (3/6) * ... * (3/60) = 1/4 * 1/5 * 1/6 * ... * 1/20

Cancelling out common factors:
Now, let's write the product in a simplified form by cancelling out the common factors:

1/4 * 1/5 * 1/6 * ... * 1/20 = (1/4 * 1/5) * (1/6 * 1/7) * ... * (1/19 * 1/20)

We can see that each fraction in the product can be written as a pair of adjacent fractions:

(1/4 * 1/5) * (1/6 * 1/7) * ... * (1/19 * 1/20) = [(1/4 * 1/5) * (1/6 * 1/7)] * ... * [(1/18 * 1/19) * (1/20)]

We can observe that each pair of adjacent fractions cancels out:

(1/4 * 1/5) * (1/6 * 1/7) * ... * (1/19 * 1/20) = 1/20

Conclusion:
The product of
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Consider a sesequence s whose nth term is defined as 1 3/n,where n=1,2,3.find the product of all consecutive terms of s starting from 4th term to 60th term?
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Consider a sesequence s whose nth term is defined as 1 3/n,where n=1,2,3.find the product of all consecutive terms of s starting from 4th term to 60th term? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Consider a sesequence s whose nth term is defined as 1 3/n,where n=1,2,3.find the product of all consecutive terms of s starting from 4th term to 60th term? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a sesequence s whose nth term is defined as 1 3/n,where n=1,2,3.find the product of all consecutive terms of s starting from 4th term to 60th term?.
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