# 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

∎