solutions for quiz xxix

X8 3 x7 x10 9 10 10 x2 x6 0 3 0 7 x3

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Unformatted text preview: x7 + x10 + · · · 9 !! 10 !! 10 ! x2 + x6 + 0 3! 0 7! x3 + x7 + + = 1 0 9! − 1 2 ·2 ·1 + 3 ·1 4 ·2 ·4 ·3 ·2 ·1 − 5 ·3 ·1 6 ·4 ·2 ·6 ·5 ·4 ·3 ·2 ·1 + 7 ·5 ·3 ·1 8 ·6 ·4 ·2 ·8 ·7 ·6 ·5 ·4 ·3 ·2 ·1 − 9 ·7 ·5 ·3 ·1 10 · 8 · 6 · 4 · 2 · 10 · 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 x9 + 3 !! 4 !! 4! 7 !! 8 !! 8! x4 x8 x10 + · · · x2 2 x4 x6 x8 x10 + · · · 1 6 ·4 ·2 ·6 ·4 ·2 1 8 ·6 ·4 ·2 ·8 ·6 ·4 ·2 − 1 10 · 8 · 6 · 4 · 2 · 10 · 8 · 6 · 4 · 2 1 1− ∞ = ℓ=0 ⋆ 1 4 ·2 ·4 ·2 + 1 1 2 ·2 − = − + = 2 !! 2 x2 x4 1 x2 + x8 1 x6 + 8 !! 2 x8 − · · · x2 ℓ . 2 2 ℓ !! Alternative Answers for (2a), (2b) : Since 2 2 ℓ !! 6 !! 2 1 ℓ x10 + · · · 1 x4 − 2 4 !! −1 x6 = ℓ! 2 · 22 ℓ , you may write your answers alternatively as ∞ (2a) Jx = ℓ=0 (2b) J x = 1 − 1 1! 2 x 2 1 ℓ −1 2 + ℓ! 1 2! 2 x 2 3 2 4 −...
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