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.

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

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

We have proven our conjecture.

  Reflect on this activity