For x [ ] R, let [x] denote the greatest integer [ ] x, then the sum of the series [[ - 1 …

Question

For x $$\varepsilon $$ R, let [x] denote the greatest integer $$ \le $$ x, then the sum of the series
$$\left[ { - {1 \over 3}} \right] + \left[ { - {1 \over 3} - {1 \over {100}}} \right] + \left[ { - {1 \over 3} - {2 \over {100}}} \right] + .... + \left[ { - {1 \over 3} - {{99} \over {100}}} \right]$$ is :

Accepted Answer

$$\left[ {{{ - 1} \over 3}} \right] + \left[ {{{ - 1} \over 3} - {1 \over {100}}} \right] + \left[ {{{ - 1} \over 3} - {2 \over {100}}} \right] +$$

$$  ....... + \left[ {{{ - 1} \over 3} - {{99} \over {100}}} \right]$$

$$ \Rightarrow ( - 1 - 1 - 1 - .....67\,times) + ( - 2 - 2 - 2 - .....33\,times)$$

$$ \Rightarrow $$ -133

Solutions · 1