Let S(K):1+3+5+…+(2K−1)=3+k2Then which of the following is true?

Let S(K):1+3+5++(2K1)=3+k2

Then which of the following is true?

  1. A

    S(K)S(K+1)

  2. B

    S(K)S(K+1)

  3. C

    S(1) is correct 

  4. D

     principle of mathematical induction can be used to prove the formula

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    Solution:

    S(1):1=3+12 which is not true. Suppose 

    S(K)  is true, then

    1+3+5++(2K1)=3+K2

    Adding (2K + 1) to both the sides, we get

    1+3+5++(2K1)+(2K+1)=3+K2+2K+1=3+(K+1)2

    which is S (K + 1)

    Thus,  S(K) fi S(K + 1).

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