Mathematics
Let us look at the triangular numbers figure again. Add two consecutive triangular numbers. For example, T1 + T2 = 4, T2 + T3 = 9, T3 + T4 = 16.
What about T4 + T5 ? Make a conjecture about Tn-1 + Tn.
Related Questions
Take any three consecutive even numbers and find their product; for example, 2 × 4 × 6 = 48, 4 × 6 × 8 = 192, and so on. Make three conjectures about these products.
Go back to Pascal’s triangle.
Line 1 : 1 = 110
Line 2 : 1 1 = 111
Line 3 : 1 2 1 = 112
Make a conjecture about Line 4 and Line 5. Does your conjecture hold? Does your conjecture hold for Line 6 too?
Look at the following pattern :
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
Make a conjecture about each of the following:
1111112 =
11111112 =
Check if your conjecture is true.
List five axioms (postulates) used in this book.