Prove that 1+14+19+116+.....+1n2<2−12 for all n>2, n ϵ N.
limn→∞1√n2−1+1√n2−4+1√n2−9+.....1√2n−1=
The value of limn→∞[n1+n2+n4+n2+n9+n2+⋯+12n] is equal to [Bihar CEE 1994]