HallsofIvy said:Well, you haven't shown that it is true for n= 1, so, no. But that is easily fixed.
Mathematical induction is a method of mathematical proof used to prove that a statement or property holds for all natural numbers. It involves proving a base case and then using a logical argument to show that if the statement holds for any given number, it also holds for the next number.
To prove a statement using mathematical induction, you must first prove that it is true for the first or smallest natural number. This is known as the base case. Then, you must show that if the statement holds for any given natural number, it also holds for the next number. This is known as the inductive step. By repeating this process, you can prove that the statement holds for all natural numbers.
The statement that needs to be proved is Sn=(-1)^n(n+1), where Sn represents a sequence of numbers starting at n=1 and going up to n=k.
The solution uses mathematical induction by first proving the base case, which is when n=1. Then, it shows that if the statement holds for any given number n=k, it also holds for the next number n=k+1. This completes the inductive step and proves that the statement holds for all natural numbers.
Proving Sn=(-1)^n(n+1) for Induction is significant because it shows that the statement holds for all natural numbers. This can be used in various mathematical proofs and applications, as well as in understanding the patterns and properties of sequences. It also demonstrates the power and usefulness of mathematical induction as a proof technique.