Question

How do you find the Maclaurin Series for `f(x)= (sinx)/x`?

Answer 1

`(sinx)/x = sum_(n=0)^oo (-1)^n x^(2n)/((2n+1)!)`

Explanation:

Consider the MacLaurin series for `sinx`:

`sinx = sum_(n=0)^oo (-1)^n x^(2n+1)/((2n+1)!)`

and divide by `x` term by term:

`(sinx)/x = sum_(n=0)^oo (-1)^n 1/x x^(2n+1)/((2n+1)!) = sum_(n=0)^oo (-1)^n x^(2n)/((2n+1)!)`