is $2\sin^2(n\pi/2)+cos(n\pi)$ convergent? divergent to $+\infty$ or $-\infty$, bounded but not convergent, or none of these

Question

What I did was graph it and it was a straight horizontal line on $y=1$. Does a straight horizontal line count as bounded? also it goes in both directions so for divergent would it be positive or negative infinity.

Can you get the first terms of the sequence? Do you see any pattern? — mfl, Mar 10 '19 at 16:27

score 1 · Answer 1 · answered Mar 10 '19 at 16:31

1

Hint : For every $x\in \mathbb R$ we have $$2\sin^2(x)+\cos(2x)=2\sin^2(x)+\cos^2(x)-\sin^2(x)=\sin^2(x)+\cos^2(x)=1$$

answered Mar 10 '19 at 16:31

Peter

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is $2\sin^2(n\pi/2)+cos(n\pi)$ convergent? divergent to $+\infty$ or $-\infty$, bounded but not convergent, or none of these

1 Answers1