Find the sum of odd integers from 1 to 2001. | vedclass

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Question

(A) The odd integers from $1$ to $2001$ are $1, 3, 5, \dots, 2001$.This sequence forms an Arithmetic Progression $(A.P.)$.Here,the first term $a = 1$

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$1002001$

Vedclass · Answer

(A) The odd integers from $1$ to $2001$ are $1, 3, 5, \dots, 2001$.This sequence forms an Arithmetic Progression $(A.P.)$.Here,the first term $a = 1$ and the common difference $d = 2$.Let $n$ be the number of terms. The $n^{th}$ term is given by $a + (n - 1)d = 2001$.$1 + (n - 1)(2) = 2001$$2(n - 1) = 2000$$n - 1 = 1000$$n = 1001$The sum of $n$ terms of an $A.P.$ is $S_n = \frac{n}{2}[a + l]$,where $l$ is the last term.$S_{1001} = \frac{1001}{2}[1 + 2001]$$S_{1001} = \frac{1001}{2} 	imes 2002$$S_{1001} = 1001 	imes 1001 = 1002001$.Thus,the sum of odd integers from $1$ to $2001$ is $1002001$.

Find the sum of odd integers from $1$ to $2001$.

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