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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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