Question

please find the answer​

Answer 1

Question :-

The value of

(1 + 1/a){1 + 1/(a - 1)}{1 + 1/(a - 2)}{1 + 1/(a - 3)}{1 + 1/(a - 4)} is

Answer :-

Value is (a + 1)/(a - 4)

Explation :-

(1 + 1/a){1 + 1/(a - 1)}{1 + 1/(a - 2)}{1 + 1/(a - 3)}{1 + 1/(a - 4)}

Let us find one by one

• 1 + 1/a

= (a + 1)/a

• 1 + 1/(a - 1)

= (a - 1 + 1)/(a - 1)

= a/(a - 1)

• 1 + 1/(a - 2)

= (a - 2 + 1)/(a - 2)

= (a - 1)/(a - 2)

• 1 + 1/(a - 3)

= (a - 3 + 1)/(a - 3)

= (a - 2)/(a - 3)

• 1 + 1/(a - 4)

= (a - 4 + 1)/(a - 4)

= (a - 3)/(a - 3)

$\mathsf{ \bigg(1 + \dfrac{1}{a} \bigg) \bigg(1 + \dfrac{1}{a - 1} \bigg) \bigg(1 + \dfrac{1}{a - 2} \bigg) \bigg(1 + \dfrac{1}{a - 3} \bigg) \bigg(1 + \dfrac{1}{a - 4} \bigg)}$

$\mathsf{= \bigg( \dfrac{a + 1}{a} \bigg) \bigg( \dfrac{a}{a - 1} \bigg) \bigg(\dfrac{a-1}{a - 2} \bigg) \bigg(\dfrac{a-2}{a - 3} \bigg) \bigg( \dfrac{a-3}{a - 4} \bigg)}$

$\mathsf{ = \bigg( \dfrac{a + 1}{a - 4} \bigg) }$