mathematical induction

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. Mathemati..

Mathematical Induction..

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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 ..

Principle of Mathematical Induction (PMI) - (i) P(1) is true (ii) P(r) is true P(r+1) is tr..

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..

For any natural number n, prove tha..

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

) The magnitude of the induced EMF is equal to the rate at which the magnetic flux linked with the circuit changes. Mathematically, Faraday's laws of electromagnetic induction do not say anything about the direction of the current. The direction is given by Lenz's la..

Self Induction - When a current is established in a conductor, a magnetic field is produced in its vicinity. We can visualize this field in terms of magnetic flux. If steady current flows the number of lines of force at a given place would remain the same. But if the current changes with ..