induction query (1 Viewer)

[sasquatch]

Ok theres a question, im not sure if what i did was right.. well i think it is..but anyway its best to check hehe.

If you have an induction question such as the following:

If u₁ = 5, u₂ = 11, and u_n = 4u_n-1 - 3u_n-2 for n >= 3, show that u_n = 2 + 3ⁿ

Is it ok to do the following:
1. Show true for n = 1
2. Show true for n = 2
3. Assume true for both n = k -1, and n = k
4. Hence show true for n = k +1 using the results of the assumptions in step 3.

So is it valid to do steps 3 and 4? Thanks...

 

[Riviet]

Yes to all 4. Proving true for n=1 and 2 is actually essential in this proof as you are making more than one assumption.

 

[sasquatch]

cool. thanks again riviet