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Question Number 164810 by tabata last updated on 22/Jan/22

$$find{n}^{th}termsof<1,0,1,0,1,0,....>$$

Commented bymr W last updated on 22/Jan/22

$$a_n=n\left(mod2\right)$$ $$a_n=\frac{1-{(-1)}^n}{2}$$ $$...$$

Commented byTawa11 last updated on 22/Jan/22

$$\mathrm{Great}\mathrm{sir}$$

Answered by alephzero last updated on 24/Jan/22

$$\cos 0=1$$ $$\cos \frac{\pi }{2}=0$$ $$\cos \pi =-1$$ $$\cos \frac{3\pi }{2}=0$$ $$\Rightarrow a_n=\mid \cos \frac{(n\pm 1)\pi }{2}\mid$$ $$\mathrm{Or}$$ $$\sin \frac{\pi }{2}=1$$ $$\sin \pi =0$$ $$\sin \frac{3\pi }{2}=-1$$ $$\Rightarrow a_n=\mid \sin \frac{n\pi }{2}\mid$$

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