Question

How do you find the maclaurin series expansion of `(e^x-1)/x`?

Answer 1

`(e^x -1)/x= 1 + x/2 + x^2 /6 +x^3 /24 +...`

Explanation:

The maclaurin series expansion of `(e^x -1)/x` can be easily determined by using the maclaurin expansion of `e^x`.
So `e^x= 1+ x+x^2/(2!) +x^3/(3!) +x^4/(4!) +..........`

`e^x -1 =x+x^2/(2!) +x^3/(3!) +x^4/(4!) +..........`

`(e^x -1)/x= 1 + x/2 + x^2 /6 +x^3 /24 +...`