I understand the rules of prooving by induction, but I can't understand the math in this equation.

If someone could explain what is happening at each step I would be very thankful.

$\displaystyle k + 1 <= 3^k +1 <= 3^k + 3^k = 2.3^k <= 3.3^k = 3^k^+^1$

The way I do math is down the page not across

1)$\displaystyle k + 1 <= 3^k +1$

is the equation $\displaystyle 3^k + 3^k$ a simplification of the RHS of the above equation (1)?

how do we get $\displaystyle 3^k + 3^k$ from $\displaystyle 3^k +1$ ??

thanks for any help.