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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

 Jul 5, 2020
 #1
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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.

 Jul 5, 2020

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