algebra precalculus - How do i do this mathematical induction question?

My question:$5+10+20+...+5(2)^{n-1} = 5(2^n -1)$

1. So first step i have to prove LHS = RHS when $n=1$, which is true.


2. Then I assume the statement is true for $n=k$



3. Since the statement is true for $n=k$ then for $n=k+1$

My workings:

$5+10+20+...+5(2)^{k-1} +5(2)^{(k+1)-1}= 5(2^{k+1} -1)$

LHS: $5(2^{k-1}) + 5(2)^k$

Then I do not know how to proceed to simplify, in general, can someone show some steps and show me how to tackle simplifying this kind of questions?

Answer

$5(2^k - 1) + 5(2^k) = 5(2^{k+1} -1)$