Question

The function f(x)=101+25x2 is represented as a power series f(x)=∑n=0[infinity]cnxn. Find the first few coefficients in the power series. Some of the other problems only ask for the nonzero coefficients, but in this problem you are supposed to include those coefficents that are 0. Also, this problem is only asking for the coefficients of the power series. It does not want you to include the x's or the powers of x.

Answer 1

`\large a_0=101,\;a_1=0,\;a_2=25,\;a_n=0\;for\;n>2`

Explanation:

Since f(x) is a polynomial, it is a power series by itself with

`\large a_0=101,\;a_1=0,\;a_2=25,\;a_n=0\;for\;n>2`

On the other hand, the representation of a function as a power series around a given point is unique. This means that these are the only possible coefficients of f as a power series around 0.