d die sum ot odd integers from 1 to 2001.d the sun of all naturalnumbe

1.	d die sum ot odd integers from 1 to 2001.d the sun of all naturalnumbers lying betwn10 aud 1000 h
Answer» The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001. This sequence forms an A.P. Here, first term, a = 1 Common difference, d = 2 Here, a+(n−1)d = 2001 => 1+(n−1)(2) = 2001 => 2n−2 = 2000 => n = 1001 Sn= n/2[2a+(n−1)d] ∴ Sn= 1001/2[2×1+(1001−1)×2] =1001/2[2+1000×2] =1001/2×2002 =1001×1001 =1002001 Hence, the sum of odd numbers from 1 to 2001 is 1002001.

d die sum ot odd integers from 1 to 2001.d the sun of all naturalnumbers lying betwn10 aud 1000 h

Answer»

The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.

This sequence forms an A.P.

Here, first term, a = 1

Common difference, d = 2

Here,

a+(n−1)d = 2001

=> 1+(n−1)(2) = 2001

=> 2n−2 = 2000

=> n = 1001

Sn= n/2[2a+(n−1)d]

∴ Sn= 1001/2[2×1+(1001−1)×2]

=1001/2[2+1000×2]

=1001/2×2002

=1001×1001

=1002001

Hence, the sum of odd numbers from 1 to 2001 is 1002001.