HOW TO PROVE THAT THESE ALGORITHMS ARE
CORRECT?
No. 1 function fib(n)
comment Return Fn
if n = 0 then return (0) else
a : = 0; b := 1; i :=2
while i < n do
c := a+b; a := b; b ;=c; i := i + 1
return(b)
No. 2 Proof for all n โ N, if 1 + x > 0, so (1 + x)n > 1 + nx
ANSWER No. 1
Recall on mathematical induction :
Claim for all n โ N,
1 + 2 + โฆ + n = ๐(๐+1)
2
When using induction to prove that some statement concerning the positive integer is true, the
following terminology is used :
1. The induction base is the proof that the statement is true fot n = 1 (or another initial
value)
2. The induction hypothesis is the assumption that the statement is true for an arbitrary n
> 1 (or another initial value)
3. The induction step is the proof that if the statement is true for n, it must be also true
for n + 1
Then
Induction base : for n = 1
