(a) Show that the Maclaurin series of the function f(x) = is E fnx" 1 – x – x? - n=1 where fr is the nth Fibonacci number, that is, fi = 1, f2 for n > 3. [Hint: Write x/(1 - x – x²) = co + c,x + c2x²...

Could you answer both a) and b) step by step in detail please? My math is p bad. Thank youuuuuu!!!!

3. [Hint: Write x/(1 - x – x²) = co + c,x + c2x² + · . . and multiply both sides of this equation by 1 – x – x².] (b) By writing f(x) as a sum of partial fractions and thereby obtaining the Maclaurin series in a different way, find an explicit formula for the nth Fibonacci number. 1, and fn = fn-1 + fn-2 = - "/>
Extracted text: (a) Show that the Maclaurin series of the function f(x) = is E fnx" 1 – x – x? - n=1 where fr is the nth Fibonacci number, that is, fi = 1, f2 for n > 3. [Hint: Write x/(1 - x – x²) = co + c,x + c2x² + · . . and multiply both sides of this equation by 1 – x – x².] (b) By writing f(x) as a sum of partial fractions and thereby obtaining the Maclaurin series in a different way, find an explicit formula for the nth Fibonacci number. 1, and fn = fn-1 + fn-2 = -