Prove an equation is equal zero in phasor form (exponential)?

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$$ Ve^{j\omega}\sum_{k=0}^{n-1} e^{jk (\frac{2\pi}{n}) } = 0$$

How Can I show that the equation will be zero? is it correct to say the exponential quantity will form a circle using Euler's Formula and therefore it is zero!

Thanks!