Let \( S(k)=1+3+5+\ldots \ldots+(2 k-1)=3+k^{2} \),
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Let \( S(k)=1+3+5+\ldots \ldots+(2 k-1)=3+k^{2} \),
\( \mathrm{P} \) then which of the following is true?
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(1) \( S(1) \) is true
(2) \( S(k) \Rightarrow S(k+1) \)
(3) \( S(k) \Rightarrow S(k+1) \)
(4) Principle of mathematical Induction can be used to prove that formula
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