Definition:

A function which is infinitely diffrenciable its "Taylor Series centered at c" is defined as the power series:

You have,

It is centered at

Then, (infinitely diffrenciable for x=2)

In general,

When evaluated at we have,

Thus, its Taylor Series is,

Which simplifies to,

Thus,

Further we can prove that the Lagrange remainder is convergent to 0, thus this power series is a representation for