Today in class, we learned about power series and how to write them. Some power series are centered at x=0. These series are defined as the infinite sum of A sub n (An) multiplied by x^n. Other series are centered at x=c and these are defined as the infinite sum of the An multiplied by (x-c)^n. When writing a power series we first make sure the given function is in the geometric series form of 1st term/ (1-ratio). Then, the rest is easy...you just write the first term in the series and multiply each of the following terms by the ratio. Remember, the absolute value of the ratio must be less than one and to find the values of the interval of convergence for the power series just solve that absolute value equation.
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