Can you use mathematical induction to prove that the sequence defined by #t_1=6# , #t_(n+1)= t_n/(3n# for all #n in ZZ^+# can be written as #t_n=18/(3^n(n-1)!# for all #n in ZZ^+#?
1 Answer
Feb 4, 2017
Proof: (By induction)
Base case: For
Inductive hypothesis: Suppose that
Induction step: We wish to show that
#=(18/(3^k(k-1)!))/(3k)#
#=18/(3*3^k*k*(k-1)!)#
#=18/(3^(k+1)*k!)#
as desired.
We have supposed true for
∎