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Let S(K)=1+3+5+...+(2K-1)=3+K². Then which of the following is true

1. Principle of mathematical induction can be used to prove the formula
2. S(K)⇒S(K+1)
3. S(K)≠S(K+1)
4. S(1) is correct

Correct answer: S(K)⇒S(K+1)

Solution

The statement S(K)⇒S(K+1) indicates that if the formula holds for K, it also holds for K+1, which is a key aspect of mathematical induction. This relationship is essential for proving the validity of the formula for all natural numbers.

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