BITSAT 2012 Paper

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.