a0, a1, a2 is a sequence such that a0 = a1 = 1 and, for n ≥ 1, an+1 = n(an + an-1)

Find a non-recursive formula for an, valid for n >= 0, and use mathematical induction to prove that your formula is correct.

Community Answer

Date" as "{:[a_(0)=1],[a_(1)=1],[a_(n+1)=n(a_(n)+a_(n-1))quad n >= 1],[a_(l)" arite of as ar an "],[a_(0)=1],[a_(1)=1],[a_(n)=(n-1)(a_(n-1)+a_(n-2))quad n >= 2]:}for{:[a_(1)=1*(a_(1)+a_(0))=1*(2)=2=2!],[a_(3)=2*(a_(2)+a_(1))=2*(2+1)=6=3!],[a_(4)=3*(a_(3)+a_(2))=3*(6+2)=24=4" ! "],[a_(9)=4*(a_(4)+a_(3))=4*(24+6)=120=5" : "]:}check of 6or n=0,1so, a_(0)=0!=1a_(1)=110=1jo it is also correct for o&lso, ... See the full answer