When k = 1, LHS = 1 but RHS = 1 + 10 = 11 ∴ T(1) is not true Let T(k) is true. That is 1+ 3+ 5+.....+ (2k -1) = k2 +10 Now, 1+3+5+.....+(2k -1)+(2k +1) = k2 +10 + 2k +1 = (k+1)2 +10 ∴ T(k +1) is true. That is T(k) is true ⇒ T(k +1) is true. But T(n) is not true for all n ÎN , as T(1) is not true.