Question

Let p = the product of all the odd integers between 500 and 598, and let q = the product of all the odd integers between 500 and 602. In terms of q , what is the value of 1p+1q ?

Answer 1

Answer:

$\frac{360000q}{359999}$

Step-by-step explanation:

p = Product of all odd integers between 500 an 598. So,

p = 501 x 503 x 505 ... x 595 x 597

q = Product of all odd integers between 500 and 602. So,

q = 501 x 503 x 505 ... x 595 x 597 x 599 x 601

From the above relations, we can see that q is equal to p multiplied by 599 and 601. i.e.

q = p x 599 x 601

or,

$p=\frac{q}{599 \times 601}$

We need to evaluate 1p + 1q in terms of q. Using the value of p from above expression, we get:

$p+q=\frac{q}{599 \times 601} + q\\\\ p+q=\frac{q+(599 \times 601q)}{599 \times 601}\\ \\ p+q=\frac{q(1+599\times601)}{599 \times 601}\\\\ p+q=\frac{360000q}{359999}$