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1-2-x-1-2-2-x-2-3-2-x-3-100-2-x-100-10100-for-x-non-negative-integers-find-the-possible-value-of-x-




Question Number 213423 by efronzo1 last updated on 05/Nov/24
  ⌊ (1/2)x−1⌋ + ⌊ (2/2)x−2⌋+⌊(3/2)x−3⌋+...+⌊((100)/2)x−100⌋ ≤10100    for x non negative integers.     find the possible value of x
$$\:\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}−\mathrm{1}\rfloor\:+\:\lfloor\:\frac{\mathrm{2}}{\mathrm{2}}\mathrm{x}−\mathrm{2}\rfloor+\lfloor\frac{\mathrm{3}}{\mathrm{2}}\mathrm{x}−\mathrm{3}\rfloor+…+\lfloor\frac{\mathrm{100}}{\mathrm{2}}\mathrm{x}−\mathrm{100}\rfloor\:\leqslant\mathrm{10100} \\ $$$$\:\:\mathrm{for}\:\mathrm{x}\:\mathrm{non}\:\mathrm{negative}\:\mathrm{integers}. \\ $$$$\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$
Answered by golsendro last updated on 05/Nov/24
$$\:\:\:\underline{ } \:\: \\ $$
Commented by hardmath last updated on 05/Nov/24
thankyou dearprofessor
$$\mathrm{thankyou}\:\mathrm{dearprofessor} \\ $$
Commented by mr W last updated on 05/Nov/24
when A≤B is given and you get  A≤C, how can you then say C≤B,  not B≤C?
$${when}\:{A}\leqslant{B}\:{is}\:{given}\:{and}\:{you}\:{get} \\ $$$${A}\leqslant{C},\:{how}\:{can}\:{you}\:{then}\:{say}\:{C}\leqslant{B}, \\ $$$${not}\:{B}\leqslant{C}? \\ $$
Commented by mr W last updated on 05/Nov/24
how can you go   from ∣z_1 +z_2 ∣≤∣z_1 ∣+∣z_2 ∣  to ⌊z_1 −z_2 ⌋≤⌊z_1 ⌋−⌊z_2 ⌋?
$${how}\:{can}\:{you}\:{go}\: \\ $$$${from}\:\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid\leqslant\mid{z}_{\mathrm{1}} \mid+\mid{z}_{\mathrm{2}} \mid \\ $$$${to}\:\lfloor{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \rfloor\leqslant\lfloor{z}_{\mathrm{1}} \rfloor−\lfloor{z}_{\mathrm{2}} \rfloor? \\ $$

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