Let $$S(k)=1+3+5+$$…$$+(2k$$−$$1)=3+k2$$ Then which of the following is true?

Correct option is 2S(k)⇒S(k+1)

Questions

Let $S (k) = 1 + 3 + 5 + \dots + (2 k - 1) = 3 + k^{2}$ Then which of the following is true?

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Principle of mathematical Induction can be used to prove the formula

S(k)⇒S(k+1)

S(1) is correct

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detailed solution

Correct option is B

Let S (k) be true. Then1+3+5+…+(2k−1)=3+k2 ....(i)Now,S(k+1)=1+3+5+…+(2k−1)+(2k+1) =3+k2+2k+1=3+(k+1)2 [Using (i)]⇒ S(k+1) is true.Hence, S(k)⇒S(k+1).

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Let S(k)=1+3+5+…+(2k−1)=3+k2 Then which of the following is true?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Let $S (k) = 1 + 3 + 5 + \dots + (2 k - 1) = 3 + k^{2}$ Then which of the following is true?