The value of \( \Large \left(1+\frac{1}{x}\right) \left(1+\frac{1}{x+1}\right) \left(1+\frac{1}{x+2}\right) \left(1+\frac{1}{x+3}\right) \) is:

A) \( \Large 1+\frac{1}{x+4} \)

B) x+4

C) \( \Large \frac{1}{x} \)

D) \( \Large \frac{x+4}{x} \)

Correct answer:
D) \( \Large \frac{x+4}{x} \)

Description for Correct answer:
\( \Large \left(1+\frac{1}{x}\right) \left(1+\frac{1}{x+1}\right) \left(1+\frac{1}{x+2}\right) \left(1+\frac{1}{x+3}\right) \)

Taking L.C.M. of each term.

=> \( \Large \left(\frac{x+1}{x}\right) \left(\frac{x+1+1}{x+1}\right) \left(\frac{x+2+1}{x+2}\right) \left(\frac{x+3+1}{x+3}\right) \)

=> \( \Large \frac{1}{x} \times \left(x+4\right) \)

=> \( \Large \frac{x+4}{x} \)


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