State the proof by Mathematical Induction of P(n), the statement that 1+3+5+ ...+(2n – 1)= n² for all integers 21 a. State the base case. Prove that the base case is true. b. Assume P((k) is true for some k>1. Show that if P(k) is true then P(k+1) is true. c. What is your conclusion? (Do not write “P(n) is true.") Restate what you needed to prove.

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Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

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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.