Let S(K):1+3+5+·s+(2K-1)=3+K². Then (a) the principle of induction proves the formula (b) S(K)→ S(K+1) (c) S(K) is true for all K (d) S(1) is correct

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[JEE Main 2004] let s k 1 3 5 2k 1 3 k 2 then

VAVidaara Admin Asked 2d ago 0 views 1 answer

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

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

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.