[JEE Main 2004] Let $S(K):1+3+5+\cdots+(2K-1)=3+K^2$. Then
Let $S(K):1+3+5+\cdots+(2K-1)=3+K^2$. Then
(a) the principle of induction proves the formula
(b) $S(K)\Rightarrow S(K+1)$
(c) $S(K)$ is true for all $K$
(d) $S(1)$ is correct
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 1mo ago
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Correct answer: (b) $S(K)\Rightarrow S(K+1)$
The inductive step holds: $S(K)\Rightarrow S(K+1)$ (adding $2K+1$). But $S(1)$ is false, so the formula itself is wrong.
JEE Main 2004 · Binomial Theorem — verified solution by the Vidaara Team.
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