​If  $$\frac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{d + \cfrac{1}{e}}}}} = \frac{421}{972}$$​ , then what is the value of a × b × c × d × e?​

Correct option is A

Given:

$$\frac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{d + \cfrac{1}{e}}}}} = \frac{421}{972}$$​

Solution:

For this type of question, we solve the reciprocal of the value and the integers will be values of the variables,

​$$\frac{972}{421} = 2 + \frac{130}{421} \Rightarrow a = 2 \\[10pt]\frac{421}{130} = 3 + \frac{31}{130} \Rightarrow b = 3 \\[10pt]\frac{130}{31} = 4 + \frac{6}{31} \Rightarrow c = 4 \\[10pt]\frac{31}{6} = 5 + \frac{1}{6} \Rightarrow d = 5$$

6/1 = 6 => e = 6

=> a × b × c × d × e = 2 × 3× 4 × 5 × 6

=> a × b × c × d × e = 720

∴ The correct answer is 720.

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