Question

2. Find a power series expression centered around a = 0 for each function, by manipulating simpler known power series. Please give your answer in sigma notation, (a) f(x) = 3 + x2 (b) f(x) = 5 - 30

Answer 1

By simpler known power series transform the given function into the simpler one.

® 69 tow a very glutning We know that its = 1-x+x2-x3 + :*(N) = (1+x)=x-+ 2)2-(2+-----.] WL 1리 ni 5-332 b) fous are t o - W.Kt task = 1+2+x++x+re+ - Efense #(1-x)* =*(1+BX+(84)*74**)*+--) . + 2x + ***+ **+ --- = 3 (5** ***)

Then express the given function as the required power series.