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Maths-

General

Easy

Question

If $1 minus fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 5 end fraction minus fraction numerator 1 over denominator 7 end fraction plus fraction numerator 1 over denominator 9 end fraction minus fraction numerator 1 over denominator 11 end fraction plus horizontal ellipsis equals fraction numerator pi over denominator 4 end fraction$ , then value of $fraction numerator 1 over denominator 1 cross times 3 end fraction plus fraction numerator 1 over denominator 5 cross times 7 end fraction plus fraction numerator 1 over denominator 9 cross times 11 end fraction plus horizontal ellipsis$ is

$π / 8$
$π / 6$
$π / 4$
$π / 36$

The correct answer is: $pi divided by 8$

We have,
$fraction numerator pi over denominator 4 end fraction equals open parentheses 1 minus fraction numerator 1 over denominator 3 end fraction close parentheses plus open parentheses fraction numerator 1 over denominator 5 end fraction minus fraction numerator 1 over denominator 7 end fraction close parentheses plus open parentheses fraction numerator 1 over denominator 9 end fraction minus fraction numerator 1 over denominator 11 end fraction close parentheses plus horizontal ellipsis$
$equals fraction numerator 2 over denominator 1 cross times 3 end fraction plus fraction numerator 2 over denominator 5 cross times 7 end fraction plus fraction numerator 2 over denominator 9 cross times 1 end fraction plus horizontal ellipsis$
$rightwards double arrow blank fraction numerator 1 over denominator 1 cross times 3 end fraction plus fraction numerator 1 over denominator 5 cross times 7 end fraction plus fraction numerator 1 over denominator 9 cross times 11 end fraction plus horizontal ellipsis equals fraction numerator pi over denominator 8 end fraction$

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