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Question Number 206992 by mnjuly1970 last updated on 03/May/24

Answered by mr W last updated on 03/May/24

$$-1⩽x^2+x<0$$$$\Rightarrow -1<x<0$$$$\Rightarrow 0<x^{2n}<1\Rightarrow \lfloor x^{2n}\rfloor =0$$$$\Rightarrow -1<x^{2n+1}<0\Rightarrow \lfloor x^{2n+1}\rfloor =-1$$$$\underset{k=1}{\sum ^{30}}\lfloor x^k\rfloor =\underset{n=1}{\sum ^{15}}\lfloor x^{2n}\rfloor +\underset{n=0}{\sum ^{14}}\lfloor x^{2n+1}\rfloor$$$$=15\times 0+15\times (-1)=-15$$

Commented by mnjuly1970 last updated on 03/May/24

$$\underset{―}{\underbrace{⋚}}$$

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