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Steps for Alternating Series Test
Suppose that we have a series ∑an and either an = (-1)n bn or an = (-1)n+1 bn where bn > 0 for all n. Then if,
1.
2. {bn} is a decreasing sequence
the series ∑an is convergent.
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sin(2x+x)=sin2x.cosx+cos2x.sinx =2sinxcosx.cosx+(-2sin^2x)sinx =2sinxcos^2+sinx-2sin^3x =sinx(2cos^2x+1)-2sin^3x =sinx(2-2sin^2x+1)-2sin^3
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