Find the sum of odd integers from 1 to 2001

Solution:

The odd integers from 1 to 2001 are 1, 3, 5, 7, 9, ...., 1999, 2001.

This sequence forms an A.P.

Here, first term, a = 1

Common difference, d = 2

Last term l = a_n = 2001

Therefore,

a_n = a + (n - 1) d

1+ (n - 1)(2) = 2001

1+ 2n - 2 = 2001

2n = 2001 + 1

n = 2002/2

n = 1001

Now,

S_n = n/2 [2a + (n - 1) d]

S₁₀₀₁ = 1001/2 [2 x 1 + (1001 - 1) x 2]

= 1001/2 [2 + 1000 x 2]

= 1001/2 x 2002

= 1001 x 1001

= 1002001

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

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.2 Question 1

Find the sum of odd integers from 1 to 2001

Summary:

Since we know that the sum of odd numbers are S_n = n/2 [2a + (n - 1) d]. The sum is 1002001