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Reasoning and ProofSession 04 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Reasoning and Proof
  Introduction | Triangular and Square Numbers | Conjecturing with Algebraic Symbols | Proving the Conjecture | Reflection Questions | Summary | Your Journal

 
 

Here is our conjecture, n (n + 1) / 2 + (n + 1) (n + 2) / 2 = (n + 1)2.


Now work on your own to prove this conjecture, when you are ready, select "Show Answer" to see our response.


1. Evaluate the expression.

Show Answer
Sample Answer:
n (n + 1) / 2 + (n + 1) (n + 2) / 2 = (n2 + n + n2 + n + 2n + 2) / 2
 

2. Simplify.

Show Answer
Sample Answer:
= (2n2 + 4n + 2) / 2
 

3. Divide by 2.

Show Answer
Sample Answer:
= n2 + 2n + 1

4. This can be written as (n + 1)(n + 1) or (n + 1)2, which is a square number.


 

We have proven our conjecture.

Next  Reflect on this activity

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