Let $A=\{1,2,3,\mathrm{........},100\}$ be a set containing n elements. The number of subsets of A having at least one odd integer is ([x] denotes greatest integer $\le x$)

Number of even integer in 1,2………n is $\left[\frac{{\displaystyle n}}{{\displaystyle 2}}\right]$.

Number of subsets having at least one odd integer

=Total number of subsets - Number of subsets of even integers $=2^n-2^{[n/2]}$