A function $f(\theta )$ is defined as $f(\theta )\, = \,1\, - \theta  + \frac{{{\theta ^2}}}{{2!}} - \frac{{{\theta ^3}}}{{3!}} + \frac{{{\theta ^4}}}{{4!}} + ...$ Why is it necessary for  $f(\theta )$  to be a dimensionless quantity ?

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Since, $f(\theta)$ is a sum of different power of $\theta$ and as $RHS$ is dimensionless, hence $LHS$ should also be dimensionless.

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