The loop below computes the sum k 1 n k 2 While ( j n ) sum sum j 2 j j 1 End while Pre condition m and n are non negative integers j 1 and sum 0 Post condition sum k 1 nk 2 Loop invariant j is an integer, j n 1 , and sum k 1 j 1 k 2 What facts are assumed in proving the post condition j is an integer j n and j n sum k 1 j 1 k 2 j is an integer j n 1 and j n sum k 1 j 1 k 2 j is an integer j n and j n sum k 1 j 1 k 2 j is an integer j n 1 and j n sum k 1 j 1 k 2

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Question: The loop below computes the sum k = 1 n k 2 : While ( j n ) sum : = sum + j ^

The loop below computes the sum

= 1

n k

2

While

(

)

sum :

=

sum

+

^2

j :

=

+ 1

End

-

while

Pre

-

condition: m and n are non

-

negative integers. j

= 1

and sum

= 0 .

Post

-

condition: sum

=

= 1

2 .

Loop

-

invariant: j is an integer, j

+ 1,

and sum

=

= 1

1

2 .

What facts are assumed in proving the post

-

condition?

j is an integer

n and j

>

sum

=

= 1

1

2

j is an integer

<

+ 1

and j

sum

=

= 1

1

2

j is an integer

n and j

sum

=

= 1

1

2

j is an integer

+ 1

and j

sum

=

= 1

1

2

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