Answer:
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...…...
Step-by-step explanation:
Suppose that f(x) and g(x) are given by the power series
f(x)=6+7x+3x2+5x3+⋯ and
g(x)=7+8x+3x2+4x3+⋯
By multiplying power series ,
f(x).g(x) = (6+7x+3x2+5x3+⋯).(7+8x+3x2+4x3+⋯)
= 6(7+8x+3x2+4x3+⋯)+7x(7+8x+3x2+4x3+⋯)+3x2(7+8x+3x2+4x3+⋯) + 5x3(7+8x+3x2+4x3+⋯)+......
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.is the form
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...……