math question and answers the number of dolphins in the ocean

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical I..

Mathematical Induction..

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Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = ..

Principle of Mathematical Induction - If P(n) is a statement (n N); such that: P(1) is true and truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n ..

Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if..

If P(n) is a statement (n N); such that 1. P(1) is true and 2. truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n ..

For any natural number n, prove tha..

(i) P(1) is true (ii) P(r) is true P(r+1) is tr..

Let n(R) = number of boys of who play rugby n(T) = number of boys who play tennis Let x = number of boys who play both the games From the above diagram it is clear that, Those who play rugby only = 60 - x = 60 - 15 = 45 Those who play tennis only = 35 - 15 =..