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Find the sum of odd integer from 1to 2001 |
| Answer» The odd integers from 1 to 2001 are 1, 3, 5 …1999, 2001.This sequence forms a Arithmetic ProgressionLet the first term be ‘a’ and common difference ‘d’.Let n be the total number of terms in the series.Here, first term, a = 1Common difference, d = 2If l denotes the last term of the seriesThen, l = a + (n – 1) × dHere, l = 2001⇒2001 = 1 + (n – 1) × 2⇒2001 – 1 = (n – 1) × 2⇒2000/2 = n – 1⇒1000 + 1 = n∴n = 1001Sum of A.P. =⇒Sn = 1002001∴The sum of odd numbers from 1 to 2001 is 1002001. | |