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Explain in Detail :Application of Mathematical Induction in Real Life – ‘The Domino Effect.’
Mathematical induction is a technique that is used to prove a statement is true for all natural numbers. The statement is first assumed to be true for a particular value of n. This is then followed by a proof that if the statement is true for n, it is also true for the next value of n, which is one more than the previous value. The proof is based on the fact that the statement is true for the first value of n, and that the next value of n is just the previous value plus one.
This technique can be used to prove a statement is true for all positive integers. The statement can be something as simple as the sum of the first n positive integers, or the product of the first n positive integers.
The Domino Effect is an example of mathematical induction in action. This phenomenon is observed when a row of dominoes is set up, and the first domino is knocked over. This then causes the next domino to fall, and so on. The Domino Effect is also known as the avalanche effect.
The Domino Effect can be explained using mathematical induction. The statement being proven is that the Domino Effect will happen for any row of dominoes, no matter how long the row is. The first step is to prove that the statement is true for the first two dominoes. This is done by showing that the sum of the first two dominoes is equal to the third domino
Mathematical Induction Example
To show that a particular statement is true for all natural numbers, we can use mathematical induction. This involves checking to see if the statement is true for the first natural number, and then checking to see if the statement is true for the next natural number, based on the assumption that the statement is true for the previous natural number.
Here is an example of how mathematical induction can be used to show that a statement is true for all natural numbers.
The statement being tested is “For any natural number n, n multiplied by 5 is always less than or equal to n plus 25.”
The first step is to check to see if the statement is true for the first natural number, n=1. In this case, n multiplied by 5 is 5, which is less than or equal to n plus 25, which is 30. Therefore, the statement is true for the first natural number.
The next step is to check to see if the statement is true for the next natural number, n=2. In this case, n multiplied by 5 is 10, which is less than or equal to n plus 25, which is 35. Therefore, the statement is true for the next natural number.
The next step is to check to see if the statement is true for the next natural number, n=3. In this case, n multiplied by 5 is 15, which is less than or equal to n plus 25, which is 40. Therefore
