Powers and Roots Practice Test 1

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Question : 18 of 40

Marks: +1, -0

The product of

(1-1/2^2)(1-1/3^2)(1-1/4^2)...

(1-1/11^2)(1-1/12^2)

is equal to:

$5/8$
$11/20$
$17/18$
$13/24$

Solution:

(1-1/2^2)(1-1/3^2)(1-1/4^2)...

(1-1/11^2)(1-1/12^2)

By using

a^2-b^2=(a-b)(a+b)

(1-1/2)(1+1/2)

(1-1/3)(1+1/3)(1-1/4)

(1+1/4)...(1-1/12)(1+1/12)

Here

(1-1/2)(1-1/3)(1-1/4)...(1-1/12)

First

=1/2×2/3×3/4×

...×11/12=1/12

...(i)
Now

(1+1/2)(1+1/3)(1+1/4)

...(1+1/12)

=2/3×4/3×5/4×...×13/12

=13/2

......(ii)
Multiplying equation (i) and (ii), we get

1/12×13/2=13/24

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