def total$\_$distance$\_$iterative$($initial$\_$height, bounciness$\_$index, num$\_$bounces$)$:

total$\_$distance $=0$

current$\_$height $=$ initial$\_$height

print$("$Equation: $",$ end$="")$

for bounce in range$($num$\_$bounces$)$:

# Distance falling down

total$\_$distance $+=$ current$\_$height

print$($f$"\{$current$\_$height:$\mathrm{.}2$f$\}",$ end$="+")$

# Distance bouncing up

bounce$\_$height $=$ current$\_$height $*$ bounciness$\_$index

total$\_$distance $+=$ bounce$\_$height

if bounce $<$ num$\_$bounces $-1$:

print$($f$"\{$bounce$\_$height:$\mathrm{.}2$f$\}",$ end$="+")$

else:

print$($f$"\{$bounce$\_$height:$\mathrm{.}2$f$\}",$ end$="=")$

# Set the current height for the next bounce

current$\_$height $=$ bounce$\_$height

print$($f$"\{$total$\_$distance:$\mathrm{.}2$f$\}$ meters"$)$

return total$\_$distance

# Example use case

initial$\_$height $=$ float$($input$("$Enter the initial height: $"))$

bounciness$\_$index $=$ float$($input$("$Enter the bounciness index: $"))$

num$\_$bounces $=$ int$($input$("$Enter the number of bounces: $"))$

total$\_$distance$\_$iterative$($initial$\_$height, bounciness$\_$index, num$\_$bounces$)$

how to Convert that program into a recursive version