Aptitude Doubt

Question

(1-1/3) (1-1/4) (1-1/5)...(1-1/n)=x then the value of x is :

a)1/n b)2/n c)2(n-1)/n d)2/n(n+1)

Comments

it is 2/n which is b

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b?

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@Deepanshu,@Shubhgupta,Both of you are right. Please provide the steps too. :)

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See except 2 in 1st term and n in last term is not canceled otherwise everything got canceled.

$\frac{2}{\not{3}} * \frac{\not{3}}{\not{4}} * \frac{\not{4}}{\not{5}}-------------------\frac{\not{(n-3)}}{\not{(n-2)}} *\frac{\not{(n-2)}}{\not{(n-1)}} * \frac{\not{(n-1)}}{n} = \frac{2}{n}$

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@Shubhgupta,Shouldn't it be 2*(n-2)/n. If I m wrong correct please?

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first term numerator and last term denominator is not canceled otherwise everything is canceled.

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@Shubhgupta,So according to you it's not taken into consideration. Right?Coz it's multiplied along side 2/n. Isn't it?

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see now i think it will be more clear.

Answer 1

The correct option is B i.e. 2/n

Because when we expand out the expression everything except 'n' in the denominator will be canceled out with everything except '2' of the numerator giving the answer as 2/n

Answer 2

Yes the correct Answer is 2/n.