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Binod Kumar

· started a discussion

· 1 Months ago

q10 kindly correct the format of question so it can be understood in solution (Question:456232.0)

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

Question:
The value of  \(\left ( 1+\frac {1}{x} \right) \left ( 1+\frac {1}{x+1} \right )\left ( 1+\frac {1}{x+2} \right ) \left ( 1+\frac {1}{x+3} \right )\) is: 
Options:
A) \(\left ( 1+\frac {1}{x+4}\right )\)
B) \(x+4\)
C) 1/x
D) \(\cfrac{x+4}{x}\)
Solution:
Ans; (d)
\(\left ( 1+\frac {1}{x} \right) \left ( 1+\frac {1}{x+1} \right )\left ( 1+\frac {1}{x+2} \right ) \left ( 1+\frac {1}{x+3} \right )\)

Taking L.C.M of each term,

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

\(\cfrac{1}{x}\times(x+4)\Rightarrow\cfrac{x+4}{x}\)

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