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

S(1):1=3+12 which is not true. Suppose S(K)  is true, then1+3+5+…+(2K−1)=3+K2Adding (2K + 1) to both the sides, we get1+3+5+…+(2K−1)+(2K+1)=3+K2+2K+1=3+(K+1)2which is S (K + 1)Thus,  S(K) fi S(K + 1).