Question

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find the sum of odd numbers from 1 to 2000

Answer 1

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The odd integers from 1 to 2001 are 1, 3, 5 ....... 1999,2001. This sequence forms an A.P.Hence, the sum of odd no.'s from 1to 2001is 1002001.

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Answer 2

The sum of odd numbers from 1 to 2000 is 998001

Given:

Odd numbers from 1 to 2000

To find:

Find the sum of odd numbers from 1 to 2000

Solution:

Given series is Odd numbers from 1 to 2000

⇒ 1, 3, 5, 7 ..... 1999 is a Arithmetic sequence

Here, first term a = 1, and common difference d = 2

Let assume that 1999 is a nth term of the sequence

As we know nth term a$_{n}$ ⇒ a+(n-1)d

⇒ 1+(n-1)2 = 1999

⇒  (n-1)2 = 2000

⇒ (n-1) = 1000

⇒ n = 999  

Therefore, number of terms in above sequence = 999

Now to find sum of odd terms, we need to find sum of 999 terms in AP

As we know sum of n terms = $\frac{n}{2} [ 2a+(n-1)d]$  

⇒ Sum of 999 terms = $\frac{999}{2} [ 2(1)+(999-1)2]$  

= $499.5[ 2+(998)2]$

= $499.5[ 2+1996]$

= $499.5[1998]$

= 998001

Therefore, The sum of odd numbers from 1 to 2000 = 998001

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