Question

Find the sum of odd integer from $1$ and $2001$.

Answer 1

The series of odd integers from 1 to 2001 is,

$1,3,5,\mathrm{7..............},2001$

$a=1$

$d=3-1=2$

$l=2001$

$a_n=a+(n-1)d$

$2001=1+(n-1)2$

$2000=2(n-1)$

$\therefore n=1001$

$S_n=\frac{n}{2}[a+l]$

$=\frac{1001}{2}[1+2001]$

$=10,02,001$