Consider the sequence of integers s(1), s(2), s(3), .... s(n)....... defined by s(1)= 1; s(n+1) = 3*s(n) +1:etc..
Now it so turns out that 2*s(n) +1 = 3^n.
I have veriffied this to be true for n= 1,2,3,4, etc.

Can someone prove as to why is this so? And is this true for all n?

Originally posted by ranjan sinha Consider the sequence of integers s(1), s(2), s(3), .... s(n)....... defined by s(1)= 1; s(n+1) = 3*s(n) +1:etc..
Now it so turns out that 2*s(n) +1 = 3^n.
I have veriffied this to be true for n= 1,2,3,4, etc.

Can someone prove as to why is this so? And is this true for all n?

Originally posted by ranjan sinha Consider the sequence of integers s(1), s(2), s(3), .... s(n)....... defined by s(1)= 1; s(n+1) = 3*s(n) +1:etc..
Now it so turns out that 2*s(n) +1 = 3^n.
I have veriffied this to be true for n= 1,2,3,4, etc.

Can someone prove as to why is this so? And is this true for all n?

Originally posted by TheMaster37 I was jsut feeling like writing it out to stay in practise. I generally find it very lazy to simply say "I have the proof".