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Calculate $\lfloor \sqrt 1 \rfloor + \lfloor \sqrt 2 \rfloor + \lfloor \sqrt 3 \rfloor + \cdots + \lfloor \sqrt {145} \rfloor$

Note: $\lfloor x \rfloor$ denotes the floor function

Guest Jul 5, 2020

Alan · Answer 1 · 2020-07-05T01:41:23

As follows:

1*3+2*5+3*7+4*9+5*11+6*13+7*15+8*17+9*19+10*21+11*23+12*2 = 1102

i.e. there are 3 ones, 5 twos, 7 threes, ... 23 elevens and 2 twelves.