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Que: If p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the product......

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by Max@Math Revolution » Fri Feb 05, 2021 10:14 pm

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Que: If p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the product of the reciprocals of integers from 150 to 251, inclusive, what is the value of \(p^{-1}+q^{-1}\) in terms of p?

(A) \(\frac{p}{251^2}\)

(B) 251 × 252 × p

(C) 252p

(D) \(\frac{252}{p}\)

(E) 251 × 252 × \(p^2\)
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Re: Que: If p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the product......

by Max@Math Revolution » Sat Feb 13, 2021 9:13 pm
Solution: p = \(\frac{1}{150}\cdot\frac{1}{151}\cdot......\cdot\frac{1}{250}\)

q = \(\left(\frac{1}{150}\cdot\frac{1}{151}\cdot......\cdot\frac{1}{250}\right)\cdot\frac{1}{251}=p\cdot\frac{1}{251}=\frac{p}{251}\).

Thus, we have \(p^{-1}+q^{-1}=\frac{1}{p}+\frac{1}{q}\)

=> \(\frac{1}{p}+\frac{251}{p}=\frac{252}{p}\)

Therefore, D is the correct answer.

Answer D
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