Maharashtra BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions3 Marks
Question
Find the sum of odd integers from 1 to 2001.
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Answer
Let the number of terms is n.
Now the sum of the series is:
1 + 3 + 5 + ... + 2001
Here,
$\text{l}=2001$ and $\text{d}=2$
Therefore,
$\text{l}=\text{a}+(\text{n}-1)\text{d}$
$2001=1+(\text{n}-1)\text{d}$
$2(\text{n}-1)=2000$
$\text{n}-1=1000$
$\text{n}=1001$
Therefore the sum of the series is:
$\text{s}=\frac{1001}{2}[2+(1001-1)2]$
$=1001^2$
$=10021001$
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