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## Sample Document Text

1
Inductive Proofs Must Have
. Base Case (value):
- where you prove it is true about the base case
. Inductive Hypothesis (value):
- where you state what will be assume in this proof
. Inductive Step (value):
- show:
. where you state what will be proven below
- proof:
. where you prove what is stated in the show portion
. this proof must use the Inductive Hypothesis sometime during
the proof
Prove this statement:
Base Case (n=1):
Inductive Hypothesis (n=p):
Inductive Step (n=p+1):
Show:
Proof:(in class)
=
+=n
i
nni
1 2
)1(
=
=
1
1
1
i
i 1
2
2
2
)11(1
2
)1( ==+=+nn
=
+=p
i
ppi
1 2
)1(
+
=
+++=1
1 2
)1)1)((1(p
i
ppi
Variations
. 2+4+6+8+.+20 = ??
. If you can use the fact:
. Rearrange it into a form that works.
. If you can't - you must prove it from scratch
=
+=n
i
nni
1 2
)1(
2
Less Mathematical Example
. If all we had was 2 and 5 cent coins, we
could make any value greater than 3.
. Base Case (n = 4):
. Inductive Hypothesis...

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