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junior college 2 | H2 Maths
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Date Posted: 1 year ago
Views: 287
The key ideas are to do this.
(a) Prove that, for every "n-th statement" being true, the subsequent "(n + 1)-th statement will also be true. This means that every statement AND its following statement is always true.
So this implies that if the 4th statement is true, then the 5th statement is also true, but by the same logic, since the 5th statement is also true, the 6th statement must also be true; once again, since the 6th statement is true, the 7th statement must also be true, and this proceeds for every integer value of n.
(b) Prove that the very first statement is true. Of course it has to start from the first statement! (This assumes n starts from 1, but if n starts from say 3, then our first statement is with n = 3 instead of n = 1)
To prove the inductive step, we must assume that a certain statement (say, n = k) is a true statement. We are trying to prove that this "hypothesis" is true by using a series of mathematical operations to show that the case n = k + 1 should appear like the n = k case (except that k is replaced by k + 1).
(a) Prove that, for every "n-th statement" being true, the subsequent "(n + 1)-th statement will also be true. This means that every statement AND its following statement is always true.
So this implies that if the 4th statement is true, then the 5th statement is also true, but by the same logic, since the 5th statement is also true, the 6th statement must also be true; once again, since the 6th statement is true, the 7th statement must also be true, and this proceeds for every integer value of n.
(b) Prove that the very first statement is true. Of course it has to start from the first statement! (This assumes n starts from 1, but if n starts from say 3, then our first statement is with n = 3 instead of n = 1)
To prove the inductive step, we must assume that a certain statement (say, n = k) is a true statement. We are trying to prove that this "hypothesis" is true by using a series of mathematical operations to show that the case n = k + 1 should appear like the n = k case (except that k is replaced by k + 1).
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done
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Finally, we can conclude that with the proving of the base case and the inductive step, the statement will be true for all values of n.
If you need further explanation, you can ask me about this.
If you need further explanation, you can ask me about this.
Date Posted:
1 year ago
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