Using Mathematical Induction to Prove a Summation Formula

[ineedhelpnow]

$S_k:5\cdot 6 +5\cdot 6^2+5\cdot 6^3+ ...+5\cdot 6^k=6(6^k-1)$$S_k:5\cdot 6 +5\cdot 6^2+5\cdot 6^3+ ...+5\cdot 6^k+ 5\cdot 6^{k+1}=6(6^k-1)+5\cdot 6^{k+1}$

what do i do now? to prove $S_{k+1}$

 

[MarkFL]

The second statement should be labeled as $S_{k+1}$ and you want the right side to be:

\(\displaystyle 6\left(6^{k+1}-1\right)\)

Can you get from what you have to there algebraically?

By the way, I am going to move this thread to the Pre-Calculus subforum and retitle it to remove the abbreviation.

 

[ineedhelpnow]

i don't know how to get there

 

[ineedhelpnow]

here's all I've done so far:

RHS
$6^{k+1}-6+5\cdot 6^{k+1}$

 

[MarkFL]

here's all I've done so far:

RHS
$6^{k+1}-6+5\cdot 6^{k+1}$

Okay, combine like terms and then factor...

 

[ineedhelpnow]

$6^{k+1}-6+5\cdot 6^{k+1}$

$[6^{k+1}+5\cdot 6^{k+1}-6$

$[6^{k+1}(1+5)]-6$

$6[6^k(6)-1]$

$6(6^{k+1}-1)$