Can someone please help me, I really don't know to do this task. It says it's a Fibonacci sequence. Anyway it could be tommorrow on my exam.

$\displaystyle a_n = {1 \over \sqrt{5}} \times \left[ \left({1 + \sqrt{5} \over 2}\right)^n - \left({1 - \sqrt{5} \over 2}\right)^n \right] $

It should be proven by induction.... I'm stuck on third step when n = k + 1.. I don't know what to do...

Help me until tommorrow please....

Thanks in advance...