Math, asked by sakshiivaidyaa, 1 year ago

find the sum of odd integers from 1 to 2001.

Answers

Answered by stuffin
5
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Answered by Anonymous
9

\textbf{\underline{\underline{According\:to\:the\:Question}}}

Odd integers

= 1, 3 , 5 , 7 , 9 ....... , 2001

Above sequence is showing that the numbers are in Arithmetic Progression

\textbf{\underline{First\;term=1}}

\textbf{\underline{Common\; Difference}}

= 3 - 1

= 2

\textbf{\underline{Using\;Formula}}

\tt{\rightarrow a_{n}=a+(n-1)d=2001}

\tt{\rightarrow a_{n}=1+(n-1)2=2001}

2n - 2 = 2000

2n = 2000 + 2

2n = 2002

\tt{\rightarrow n=\dfrac{2002}{2}}

n = 1001

\tt{\rightarrow S_{n}=\dfrac{n}{2}[2a+(n-1)d]}

\tt{\rightarrow S_{1001}=\dfrac{1001}{2}[2(1)+(1001-1)2]}

\tt{\rightarrow S_{1001}=\dfrac{1001}{2}[2+1000\times 2]}

\tt{\rightarrow S_{1001}=\dfrac{1001}{2}\times 2002}

= 1001 × 1001

= 1002001

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