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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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Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
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Solve the subsequent IVP. y'' - 4y' + 9y = 0, y(0) = 0, y'(0) = -8 Solution The characteristic equation for such differential equation is. As: r 2 - 4r + 9 = 0
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