Floor Function Sum?

Algebra Level 3

Let x \left\lfloor x \right\rfloor denote the greatest integer less than or equal to x x . Find the value of 2 5 + 4 5 + 6 5 + . . . + 48 5 \left\lfloor \frac { 2 }{ 5 } \right\rfloor +\left\lfloor \frac { 4 }{ 5 } \right\rfloor +\left\lfloor \frac { 6 }{ 5 } \right\rfloor +...+\left\lfloor \frac { 48 }{ 5 } \right\rfloor .

Do not use a calculator and try to do it under 5 minutes.


The answer is 110.

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