HW5sol - . Sec 1.6 p. 2 Let us rst parameterize the line...

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P ROBLEM SET 5 Partial solution Sec 2.2 p. 2 Using the ratio test we compute R = lim k →∞ ( k !) 2 (2 k )! (( k +1)!) 2 (2 k +2)! = lim k →∞ (2 k + 2)(2 k + 1) ( k + 1)( k + 1) = 4 Sec 2.2 p. 8 z 2 cos z = z 2 (1 - z 2 2! + z 4 4! - z 6 6! + ··· ) = X k =0 ( - 1) k z 2 k +2 (2 k )! . Sec 2.2 p. 10 1 + z 1 - z = (1 + z )(1 + z + z 2 + z 3 + ··· ) = 1 + X k =1 2 z k
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Unformatted text preview: . Sec 1.6 p. 2 Let us rst parameterize the line segment from to z : For t [0 , 1] let ( t ) = z t . Then Z e z dz = Z 1 e z t z dt = e z t 1 = e z-1...
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