Let R [ X ] {\displaystyle {}\mathbb {R} [X]} be the polynomial ring over R {\displaystyle {}\mathbb {R} } . For n ∈ N {\displaystyle {}n\in \mathbb {N} } , set
Show that F n {\displaystyle {}F_{n}} , n ∈ N {\displaystyle {}n\in \mathbb {N} } , is a basis of R [ X ] {\displaystyle {}\mathbb {R} [X]} .