Please modify my MIPS program such that my compute$\_$series subroutine will deal with floating numbers instead of an integer. Example of what i want my subroutine to compute is shown in the image that i sent. $(S=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...\frac{1}{n})$

My MIPS Program:

$.$data

array: $.$space $1000$ # Reserve space for the array

array$\_$size: $.$word $0$ # Variable to track the size of the array

message$\_$empty: $.$asciiz "Array is empty"

message$\_$prompt: $.$asciiz "Enter the end of the series: $"$

message$\_$menu: $.$asciiz "Main Menu

$1.$ Compute a series of numbers

$2.$ Deal with array

$0.$ Exit

Enter your choice: $"$

message$\_$submenu: $.$asciiz "Array Menu

$1.$ Add number to array

$2.$ Print array

$3.$ Back to main menu

Enter your choice: $"$

$.$text

$.$globl main

main:

# Initialize array$\_$size to $0$

li $t$0,0$

sw $t$0,$ array$\_$size

main$\_$menu:

# Display the main menu and get user input

li $v$0,4$

la $a$0,$ message$\_$menu

syscall

# Read user choice

li $v$0,5$

syscall

move $t$1,$ $v$0$ # Store user choice

# Handle user choice

beq $t$1,0,$ exit$\_$program

beq $t$1,1,$ compute$\_$series

beq $t$1,2,$ array$\_$menu

j main$\_$menu # Return to main menu if invalid choice

compute$\_$series:

# Prompt user for series end

li $v$0,4$

la $a$0,$ message$\_$prompt

syscall

# Read series end from user

li $v$0,5$

syscall

move $t$2,$ $v$0$ # Store series end

# Compute series: $1/1+1/2+...+1/$n

li $t$0,0$ # Initialize sum to $0$

li $t$3,1$ # Initialize loop counter to $1$

compute$\_$loop:

bgt $t$3,$ $t$2,$ compute$\_$done # Exit loop if counter $>$ series end

# Calculate $1/$n

move $t$4,$ $t$3$ # Store counter value in $t$4$

li $t$5,1$ # Numerator is always $1$

div $t$5,$ $t$4$ # Divide $1$ by counter

add $t$0,$ $t$0,$ $t$2$ # Add result to sum

addi $t$3,$ $t$3,1$ # Increment counter

j compute$\_$loop

compute$\_$done:

# Display the sum

li $v$0,1$

move $a$0,$ $t$0$

syscall

j main$\_$menu # Return to main menu

array$\_$menu:

# Display array menu and get user input

li $v$0,4$

la $a$0,$ message$\_$submenu

syscall

# Read user choice

li $v$0,5$

syscall

move $t$1,$ $v$0$ # Store user choice

# Handle user choice

beq $t$1,1,$ add$\_$to$\_$array

beq $t$1,2,$ print$\_$array

beq $t$1,3,$ main$\_$menu

j array$\_$menu # Return to array menu if invalid choice

add$\_$to$\_$array:

# Prompt user to enter a number

li $v$0,4$

la $a$0,$ message$\_$prompt

syscall

# Read user input $($number$)$

li $v$0,5$

syscall

move $t$2,$ $v$0$ # Store user input

# Store number in the array

lw $t$3,$ array$\_$size # Load current size of array

sw $t$2,$ array$($$t$3)$ # Store number in array at index $($size$)$

addi $t$3,$ $t$3,1$ # Increment array size

sw $t$3,$ array$\_$size # Update array size

j array$\_$menu # Return to array menu

print$\_$array:

# Check if array is empty

lw $t$3,$ array$\_$size # Load current size of array

beqz $t$3,$ print$\_$empty # If size is $0,$ array is empty

# Print array elements

li $t$4,0$ # Initialize loop counter to $0$

print$\_$loop:

bge $t$4,$ $t$3,$ array$\_$printed # Exit loop if counter $>=$ array size

# Load array element and print

lw $a$0,$ array$($$t$4)$

li $v$0,1$

syscall

addi $t$4,$ $t$4,1$ # Increment counter

j print$\_$loop

array$\_$printed:

j array$\_$menu # Return to array menu

print$\_$empty:

# Print "Array is empty"

li $v$0,4$

la $a$0,$ message$\_$empty

syscall

j array$\_$menu # Return to array menu

exit$\_$program:

# Exit program

li $v$0,10$

syscall

Please show full code.