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We are asked to find the Maclaurin series for a function involving

`cos(x)`

. Recall the Maclaurin series for

`cos(x)`

.

`cos(x)=\sum_(n=0)^(\infty ) (-1)^(n)(x^(2n))/((2n)!)`

The same equality would be true for any variable, and in particular for

`u=(1)/(14)x^(2)`

. Therefore, the Maclaurin series for

`cos((1)/(14)x^(2))`

is

`\sum_(n=0)^(\infty ) (-1)^(n)((x)^(2n))/((2n)!)=\sum_(n=0)^(\infty ) (-1)^(n)(x^(4n))/((2n)!)`