Chapter 8: Infinite Sequences and Series
Section 8.5: Taylor Series
Obtain the Maclaurin series for x2cos2 x by manipulating the series for cosx.
Obtain the Maclaurin series for x2 cos2 x
Write x2 cos2 x.
Context Panel: Series≻Formal Power Series
x2 cos2 x→formal series∑n=0∞−1n⁢4n⁢x2⁢n+22⁢n!
Obtain the Maclauring series for cosx
In the series for cosx, replace x with 2 x and multiply the series termwise by x2
Expression palette: Evaluation template
Context Panel: Simplify≻Assuming Integer
x2⋅(x2 n2 n!x=a|f(x)x=2 x) = x2⁢2⁢x2⁢n2⁢n!→assuming integerx2⁢n+2⁢4n2⁢n!
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