Question Number 190818 by cortano12 last updated on 12/Apr/23
$$\:\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{set}\:\mathrm{A}=\left\{\mathrm{1}\:,\:\mathrm{2},\:\mathrm{3},\:…,\:\mathrm{100}\right\} \\ $$$$\:\mathrm{The}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{subsets}\:\mathrm{of}\:\mathrm{A}\:\mathrm{which}\:\mathrm{when}\: \\ $$$$\:\mathrm{added}\:\mathrm{together}\:\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{4} \\ $$
Commented by safojontoshtemirov last updated on 12/Apr/23
![[((100)/4)]=25](https://www.tinkutara.com/question/Q190821.png)
$$\left[\frac{\mathrm{100}}{\mathrm{4}}\right]=\mathrm{25} \\ $$
Commented by cortano12 last updated on 12/Apr/23
$$\mathrm{no} \\ $$
Commented by mehdee42 last updated on 12/Apr/23
$$\mathrm{2}^{\mathrm{25}} −\mathrm{1} \\ $$
Commented by cortano12 last updated on 13/Apr/23
$$\mathrm{how} \\ $$
Commented by safojontoshtemirov last updated on 13/Apr/23
![formulas:2^([(n/k)]) −1 int[(n/k)]](https://www.tinkutara.com/question/Q190852.png)
$${formulas}:\mathrm{2}^{\left[\frac{{n}}{{k}}\right]} −\mathrm{1}\:\:\:\:\:{int}\left[\frac{{n}}{{k}}\right] \\ $$