If you times by another 3 you just increaase the power by 1 ie (n-1) becomes n.

Bob

]]>It's just a matter of multiplying out the bracket( by 3)

Bob

]]>How did you get rid of the n-1 in that step?

]]>k=1

But you want T(1) = 2 ???

Let's see what is happening here.

term to term rule:

so if T(1) = 2

T(2) = 3x2 + 2 = 8

T(3) = 3x8 + 2 = 26

T(4) = 3x26 + 2 = 80

........................

So did you mean

Try again k=1

That's better.

Now for the induction step

assume

use the term to term rule

This has the right form, so the induction step is complete.

Bob

]]>Hi, I am stuck on the last step. What am I supposed to do now?

Problem:

Let T(n)=3T(n-1)+2, T(1)=2. Prove by induction that T(n)=3^(n-1)Here is what I have so far:

Show base case k=1: T(1) = 3^1 - 1 = 2

If T(1) = 2 and if the proposed formula is as you've posted, then T(n) for n = 1 is 3^(1-1) = 3^(0) = 1, not 2. So the base step fails.

You appear, in your work, to have used a different formula from that which was proposed. Is there perhaps a typo somewhere?

]]>Problem: *Let T(n)=3T(n-1)+2, T(1)=2. Prove by induction that T(n)=3^(n-1)*

Here is what I have so far:

Show base case k=1: T(1) = 3^1 - 1 = 2

Show for k=n-1: T(n-1) = (3^((n-1)-1)) -1

Show for k=n :

3((3^(n-2)) - 1) + 2