Question

1) Find the sum of first 1000 positive integers.
Activity :- Let 1+2+3+ ------+1000
Using formula for the sum of first n terms of an A.P.
Sn=
S1000 = (1+1000)
= 500 * 1001
Therefore, Sum of the first 1000 positive integer is​

Answer 1

SOLUTION

TO DETERMINE

The sum of first 1000 positive integers

FORMULA TO BE IMPLEMENTED

For an arithmetic progression with

Sum of first n terms

$\displaystyle \sf{ = \frac{n}{2} \times \bigg [First \: term + Last \: term \bigg] }$

EVALUATION

Here we have to find the sum of first 1000 positive integers

So the progression is

1 + 2 + 3 + ------ + 1000

This is an arithmetic progression

First term = a = 1

Last term = 1000

Number of terms = n = 1000

So the sum of first 1000 positive integers

$\displaystyle \sf{ = \frac{n}{2} \times \bigg [First \: term + Last \: term \bigg] }$

$\displaystyle \sf{ = \frac{1000}{2} \times \bigg [1 + 1000 \bigg] }$

$\displaystyle \sf{ = 500 \times 1001 }$

$\displaystyle \sf{ = 500500 }$

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