EXERCISE A1.3
con
1. Take any three consecutive even numbers and find their product; for example,
2x4x6 = 48,4% 6% 8 192, and so on. Make three conjectures about these products,
2. Go back to Pascal's triangle.
Line 1:1 = 11°
Line 2:11-11'
Line 3:12 1 - 112
Make a conjecture about Line 4 and Line 5. Does your conjecture holdy Does your tes
conjecture hold for Line 6 too?
3. Let us look at the triangular numbers (see Fig. A1.2) again. Add two consecutive got
triangular numbers. For example, T, +T,-4,T,+T -9,T,+T. - 16.
What about T. +T,? Make a conjecture about T. +T
4. Look at the following patter:
- 1=1
112-121
1112-12321
11112 = 1234321
11111-123454321
Make a conjecture about each of the following:
111111
11111112=
Check if your coniecture is true
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