Unformatted text preview: , Ix = (1 _ .::. + x 2 _ x 3 + ... ) (1 + x + x 2 + x 3 + ... ) I! 2! 3! 1 2 1 1 3 1 + Ox + (1  1 + 2!)x + (1  1 + 2! 3!)x + ... +(11 + ~ ~ + ... + (_I)n~)xn + ... Dn/n! .368056 .367857 .367882 .367879 .367879 and we note that for any n ;:::: 0, the coefficient of xn is ~ by Proposition 7.6.2. Exercises 7.7 1. (a) [BB] (x + y)6 x 6 + 6x 5 y + 15x 4 y2 + 20x 3 y3 + 15x 2 y4 + 6xy5 + y6 (b) [BB] (2x + 3y)6 = (2x)6 + (~)(2x)5(3y) + (~)(2x)4(3y)2 + (~)(2x)3(3y)3 +(~)(2X)2(3y)4 + (~)(2x)(3y)5 + (3y)6 64x 6 + 6(32x5) (3y) + 15(16x4)(9y2) + 20(8x3) (27y3) +15(4x2)(81y4) + 6(2x)(243y5) + 729y6 64x 6 + 576x 5 y + 2160x4y2 + 4320x 3 y3 + 4860x2y4 +2916xy5 + 729y6 203...
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 Summer '10
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 Graph Theory, Trigraph, Dn

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