Induction Question (1 Viewer)

js992 · Mar 8, 2010

$\100dpi $ A sequence is such that $T_{1}=8, T_{2}=34 $ and for all positive integers n, T_{n+2} = 8T_{n+1}-15T_{n}$\\ $Prove by mathematical induction that T_{n}=3^n+5^n$$

I've worked it out but theres one step im not too sure of. When proving true for n= k+1.
$\100dpi LHS\\ = T_{k+1}\\ = 8T_{k}-15T_{k-1} $ (Given information)$\\ $ Are you allowed to assume that T_{k-1} = 3^{k-1}+5^{k-1}$\\ $ based on your assumption?$$

If not, how do i find out what T(k-1) is?

untouchablecuz · Mar 9, 2010

yes you are

this is a stronger type of induction called "strong induction" (lol)

not only do you assume S(k) to be true but rather, you assume S(1), S(2)...S(k) to be true

google for more info

also, this type of Q is out of the MX1 syllabus

cutemouse · Mar 9, 2010

To me there's no difference between the supposed 'strong' and 'weak' variations of induction...

Induction Question (1 Viewer)

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