The odd numbers from
![\[1\text{ }to\text{ }2001\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7eb75344bf6d217d070161237c820970_l3.png "Rendered by QuickLaTeX.com")
are
![\[~1,\text{ }3,\text{ }5,\text{ }\ldots \text{ }1999,\text{ }2001.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-26ba1cb0cb1fdf5994d2d807543ffc88_l3.png "Rendered by QuickLaTeX.com")
It obviously shapes an arrangement in
![\[A.P.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-48cfffb2cff49221d30490bc193b5300_l3.png "Rendered by QuickLaTeX.com")
Where, the initial term,
![\[a\text{ }=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-60007b777d643ba9eb870e9785edbbb6_l3.png "Rendered by QuickLaTeX.com")
Normal distinction,
![\[d\text{ }=\text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4bf87efb0616fc6114a70a56d16a1e90_l3.png "Rendered by QuickLaTeX.com")
Presently,
![\[\begin{array}{*{35}{l}} a\text{ }+\text{ }\left( n\text{ }-1 \right)d\text{ }=\text{ }2001 \\ 1\text{ }+\text{ }\left( n-1 \right)\left( 2 \right)\text{ }=\text{ }2001 \\ 2n\text{ }\text{ }2\text{ }=\text{ }2000 \\ 2n\text{ }=\text{ }2000\text{ }+\text{ }2\text{ }=\text{ }2002 \\ n\text{ }=\text{ }1001 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dddbfc10f737ce58bc6d412d877865e4_l3.png "Rendered by QuickLaTeX.com")
We know,
![\[{{S}_{n}}~=\text{ }n/2\text{ }\left[ 2a\text{ }+\text{ }\left( n-1 \right)d \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-417bcd262acac9d2f45730b4735d433e_l3.png "Rendered by QuickLaTeX.com")
Thus, the amount of odd numbers from
![\[1\text{ }to\text{ }2001\text{ }is\text{ }1002001.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e484f3c98028fd2d5ab772c735e35cec_l3.png "Rendered by QuickLaTeX.com")
The odd numbers from
are
It obviously shapes an arrangement in
Where, the initial term,
Normal distinction,
Presently,
We know,
Thus, the amount of odd numbers from
