# Thread: [SOLVED] Proof by induction help needed (urgently)

1. ## [SOLVED] Proof by induction help needed (urgently)

This is question 4 on June 2008 Further Pure 1 paper OCR (downloadable for OCR website) OCR > Qualifications > By type > AS/A Level GCE (current) > Mathematics > Mathematics > All documents

The question goes:
The Matrix A is given by A =

3, 1,
0, 1,

prove by induction that for n>1

A^n =

3^n, 0.5(3^n -1),
0, 1,

I just dont get how 3^k + 0.5(3^k -1) becomes 0.5(3^k+1 -1)

Thanks

2. Originally Posted by suf
...
I just dont get how 3^k + 0.5(3^k -1) becomes 0.5(3^k+1 -1)

Thanks
Simplify the expression: $3^k + \frac{1}{2} 3^k - \frac{1}{2}$

3. Thats what im having probelms with

4. Originally Posted by slider142
Simplify the expression: $3^k + \frac{1}{2} 3^k - \frac{1}{2}$
$3^k + \frac{1}{2}\cdot 3^k - \frac{1}{2} = \left(1 + \frac{1}{2}\right)3^k - \frac{1}{2}$

$= \frac{3}{2}\cdot 3^k - \frac{1}{2}$

$= \frac{1}{2}\cdot 3^{k + 1} - \frac{1}{2}$

$= \frac{1}{2}(3^k - 1)$.