Q. 20 B4.0( 4 Votes )

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

Answer :

The odd numbers lying between 1 and 2001 are


1, 3, 5,…, 2001


a2 – a1 = 3 – 1 = 2


a3 – a2 = 5 – 3 = 2


a3 – a2 = a2 – a1 = 2


Therefore, the series is in AP


Here, a = 1, d = 2 and an = 2001


We know that,


an = a + (n – 1)d


2001 = 1 + (n – 1)2


2001 – 1 = (n – 1)2


2000 = (n – 1)2


1000 = (n – 1)


n = 1001


Now, we have to find the sum of this AP




S1001 = 1001[1 + 1000]


S1001 = 1001 [1001]


S1001 = 1002001


Hence, the sum of all odd numbers lying between 1 and 2001 is 1002001.


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