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Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is

$$x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}$$

The same function $x(t)$ can also be considered as a periodic function with period ${T}'=40.$

Let $b_{k}$ be the Fourier series coefficients when period is taken as ${T}'$ . If $\sum _{k=-\infty}^{\infty } \mid a_{k} \mid =16,$ ,then $\sum _{k=-\infty}^{\infty } \mid b_{k} \mid$ is equal to

1. $256$
2. $64$
3. $16$
4. $4$