A) 1
B) 39
C) \[\frac{1}{40}\]
D) 2
Correct Answer: A
Solution :
\[\left( 1+\frac{1}{2} \right)\left( 1+\frac{1}{3} \right)\left( 1+\frac{1}{4} \right)...\left( 1+\frac{1}{40} \right)=\frac{x}{40}\] \[\Rightarrow \] \[\left( \frac{2-1}{2} \right)\times \left( \frac{3-1}{3} \right)\times \left( \frac{4-1}{4} \right)\times ..\times \left( \frac{40-1}{40} \right)\] \[=\frac{x}{40}\] \[\Rightarrow \] \[\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ...\times \frac{39}{40}=\frac{x}{40}\] \[\Rightarrow \] \[\frac{1}{40}=\frac{x}{40}\] \[\Rightarrow \] \[x=1\]
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