Question

Consider the sequence 2;3;5;6;7;8;10;::: of all positive integers that are not perfect squares. Determine the 2011th term of this sequence.

Answer 1

@oldrin.bataku

Answer 2

Find the number of perfect squares under 2011 -- this is the difference between 2011 and our number.

Answer 3

Well, we know \(\sqrt{2011}\approx45\) with rounding (since \(44^2=1936\), \(45^2=2025\)). This means we have skipped \(45\) square numbers at this point, so our 2011th term is \(2011+45=2056\)