ELEME 4. Prove that the square of any odc specifically, that In the sequence of triangular nu (a) Two triangular numbers whe (b) Three successive triangular (c) Three successive triangular 6. (a) If the triangular number t, is (b) Use part (a) to find three exa 7. Show that the difference between always a cube. & Prove that the sum of the reciproc is, 1 1 [Hint: Observe that = 2(- (a) Establish the identity t = ty + n(n + 3) and n > 1, thereby proving that the sum of two other such numb O Find three examples of triangu. numbers. ch of the numbers 1,5 1+4, 12 = 1 %3D sents the number of dots that can
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
2.1 question 8
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