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Differential Calculus

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6 Mar 2008 14:26:14 IST

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370

Taylor Expansion

None

Find the coefficient of x⁴ in the expression:

1 + (1+x+x²) + (1+x+x²)²/2! + (1+x+x²)³/3!+....

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anchit saini

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6 Mar 2008 16:10:39 IST

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EDIT!!!!

Nadeem

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6 Mar 2008 16:55:29 IST

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the given expression is the expansion of e^{( 1+ x + x2)} . this can be written as e e^xe^x2

This can be expanded as e ( 1+ x + x² /2 ! + x³ / 3! + x⁴ / 4!.....) ( 1 + x² + x⁴/2! + x⁶/3!...)

coefficient of x⁴ is e/ 4! + e/ 2! + e / 2! = e/24 + e = 25e/24

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