taylor approximation using mathematica [closed]

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For a homework assignment:

Given the Taylor expansion for Exp[x/3]

write y[x]= Summation( n>=0 ) ( (a subscript n) * x^n ) .

Solve for the coefficients (a subscript n) up to order 10.

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CoefficientList[Series[Exp[x/3], {x, 0, 10}], x]

==> {1, 1/3, 1/18, 1/162, 1/1944, 1/29160, 1/524880, 1/11022480, \
1/264539520, 1/7142567040, 1/214277011200}

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(a[#]=SeriesCoefficient[Exp[x/3],{x,0,#}])&/@Range[0,10];??a

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googling for mathematica power series

http://reference.wolfram.com/mathematica/tutorial/PowerSeries.html

You will find Mathematica's help very thorough. You can access it from the Help menu, or by evaluating the following expression:

?Series

(or whatever you're interesting in the help for)