1) Find the sum of first 1000 positive integers.
Activity :- Let 1+2+3+ ——+1000
Using formula for the sum of first n

2 thoughts on “1) Find the sum of first 1000 positive integers.<br />Activity :- Let 1+2+3+ ——+1000<br />Using formula for the sum of first n”

1. Answer is 500500
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2. SOLUTION

   TO DETERMINE

   The sum of first 1000 positive integers

   FORMULA TO BE IMPLEMENTED

   For an arithmetic progression with

   Sum of first n terms

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

   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

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

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

   [tex]\displaystyle \sf{ = 500 \times 1001 }[/tex]

   [tex]\displaystyle \sf{ = 500500 }[/tex]

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