find all x in [0,2π] for which the series ∑ (sin x)^n converges.?
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find all x in [0,2π] for which the series ∑ (sin x)^n ( from n=1 to infinity) converges.
Update:if we suppose the series like this ∑(cos x)(sin x)^n ( from n=1 to infinity)
in this case how can i solve it ?
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How can it be that one can study math and not be able to answer such a trivial question??
Geometric series converge if and only if the common ratio is strictly less than 1 in absolute value---anyone having taken a precalculus course knows this.
|sin(x)| < 1
if 0 ≤ x < π/2, or π/2 < x < 3π/2, or 3π/2 < x ≤ 2π. So it converges at all x in [0, 2π] except π/2 and 3π/2.