Find the sum of integers from 1to2001

1.	Find the sum of integers from 1to2001
Answer» Or u can use the second formula for calculating sum which is-Sn=n/2[a+l]So,from above u can see yogita has already finded the value of n which is 1001 and here u have l=2001 so,Sn=1001/2[1+2001]=1001*1001=1002001. #Ans 2003001 In this question AP has been formed, which is 1,2,3,4,5,.....,2001, in which a = 1, d = a2-a1 = 2-1 = 1, l = 2001, n = 2001S2001 = n/2(a+l) =2001/2(1+2001) =2003001, Answer Hence, the sum of integers from 1 to 2001 is 2003001. The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.This sequence forms an A.P.Here, first term, a = 1Common difference, d = 2Here,a+(n−1)d=2001=>1+(n−1)(2)=2001=>2n−2=2000=>n=1001Sn= n2[2a+(n−1)d]∴Sn= 10012[2×1+(1001−1)×2]= 10012 [2+1000 × 2]=10012×2002=1001×1001=1002001Thus, the sum of odd numbers from 1 to 2001 is 1002001.

Discussion