Powers and Roots Practice Test 2

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Question : 28 of 40

Marks: +1, -0

The value of

(1^2-1/3^2)(1^2-1/4^2)(1^2-1/5^2)

...(1^2-1/100^2)

is equal to:

$101/ 150$
$7 /150$
$9/ 200$
$3 /100$

Solution:

(1^2-1/3^2)(1^2-1/4^2)(1^2-1/5^2)

...(1^2-1/100^2)

By using

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

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

(1-1/4)(1+1/4)(1-1/5)

(1+1/5)...(1-1/100)(1+1/100)

Now

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

(1-1/5)...(1-1/100)

=2/3×3/4×4/5×...×9/100

=2/100

......(i)

(1+1/3)(1+1/4)(1+1/5)...(1+1/100)

=4/3×5/4×6/5×...×101/100=101/3

......(ii)
Now multiplying equation (i) and (ii) we get,

=2/100×101/3=101/150

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