A) and (ii) are true while (iii) is false.
B) and (iii) are true while (ii) is false.
C) (ii) and (iii) are true while (i) is false.
D) Neither (i) and (ii) nor (iii) is true.
Correct Answer: A
Solution :
(i) \[\left( 1-\frac{1}{2} \right)\,\left( 1-\frac{1}{3} \right)\,\left( 1-\frac{1}{4} \right)\,.........\left( 1-\frac{1}{x} \right)\] \[=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \,.........\times \frac{x-1}{x}=\frac{1}{x}\] (ii) \[2=x+\frac{1}{1+\frac{1}{\frac{12+1}{4}}}\,\,\,\,\,\,\,\,\,=x+\frac{1}{1+\frac{1}{\frac{13}{4}}}\] \[=x+\frac{1}{\frac{13+4}{13}}=x+\frac{13}{17}\] \[\therefore \,\,\,\,\,\,\,\,\,\,x=12-\frac{13}{17}=\frac{21}{17}\] (iii) \[(999\times 6)\,+\left( \frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7} \right)\] \[=5994+\frac{21}{7}\,=5994+3=5997\]You need to login to perform this action.
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