Powers and Roots Practice Test 3

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Question : 6 of 40

Marks: +1, -0

The value of

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

...(1-1/19^2)(1-1/20^2)

is equal to:

$21/20$
$31/40$
$21/40$
$31/40$

Solution:

(1-1/2^2)(1-1/3^2)...(1-1/20^2)

=(12-1/2^2)(1^2-1/3^2)...(1^2-1/20^2)

By using

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

(1-1/2)(1+1/2)(1-1/3)(1+1/3)

...(1-1/20)(1+1/20)

So,

(1-1/2)(1-1/3)...(1-1/20)

=1/2×2/3×3/4×....×19/20=1/20

...(1)
and

(1+1/2)(1+1/3)...(1+1/20)

=3/2×4/3×...×21/20=21/2

...(2)
Now multiplying equation (1) and (2) we get,

1/20×21/2=21/40

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