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Maths-

General

Easy

Question

Period of f (x) = sin x + tan $fraction numerator x over denominator 2 end fraction$ + sin $fraction numerator x over denominator 2 to the power of 2 end exponent end fraction$ + tan $fraction numerator x over denominator 2 to the power of 3 end exponent end fraction$ + ... + sin $fraction numerator x over denominator 2 to the power of n minus 1 end exponent end fraction$ + tan $fraction numerator x over denominator 2 to the power of n end exponent end fraction$ is -

$\frac{π}{2}$
$π$
$2^{n} π$
$\frac{2 π}{5}$

The correct answer is: $2 to the power of n end exponent pi$

STEP BY STEP SOLUTION
Period of f (x) = sin x + tan $fraction numerator x over denominator 2 end fraction$ + sin $fraction numerator x over denominator 2 to the power of 2 end exponent end fraction$ + tan $fraction numerator x over denominator 2 to the power of 3 end exponent end fraction$ + ... + sin $fraction numerator x over denominator 2 to the power of n minus 1 end exponent end fraction$ + tan $fraction numerator x over denominator 2 to the power of n end exponent end fraction$ is
Period of $open parentheses sin x space plus space tan space x over 2 close parentheses space i s space 2 straight pi space comma$
$open parentheses sin space x over 2 squared space plus space tan space x over 2 cubed close parentheses space i s space 2 cubed straight pi open parentheses sin space straight x over 2 to the power of straight n minus 1 end exponent space plus space tan space straight x over 2 to the power of straight n close parentheses space is space 2 to the power of straight n straight pi And space so space on space for space consecutive space terms space LCM space of space open curly brackets 2 straight pi comma 2 to the power of 3 space end exponent straight pi comma...... comma 2 to the power of straight n straight pi close curly brackets space equals space 2 to the power of straight n straight pi Hence comma space the space period space of space straight f left parenthesis straight x right parenthesis space is space 2 to the power of straight n straight pi$

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