The value of (1+1/x)(1+1/(x+1))(1+1/(x+2))(1+1/(x+3)) is equal to _____?
- 1/x
- x+4/x
- x+4
- None of these
Explanation
(1 + 1/x)(1 + 1/(x+1))(1 + 1/(x+2))(1 + 1/(x+3))
= ((x+1)/x)((x+2)/(x+1))((x+3)/(x+2))((x+4)/(x+3))
Notice that the denominators and numerators cancel out:
= (x+4)/x
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