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The sum of products of 2n numbers ± 1, ± 2 , ± 3, ± 4... ± n taking two at a time is a) – ∑ r=1 n r ​b) ∑ r=1 n r^2 ​c) – ∑ r=1 n r^2 d)none of these Please explain the question and and its solution.. What does the question ask??

The sum of products of 2n numbers ± 1, ± 2 , ± 3, ± 4... ± n taking two at a time  is
a) – ∑r=1n r
​b)r=1r^2
​c) – r=1n r^2
d)none of these
Please explain the question  and and its solution..
What does the question ask?? 

Grade:

1 Answers

Aditya Gupta
2075 Points
2 years ago
we know that 
(a1+a2+a3+......+am)^2= sum of squares of all the terms + 2*(sum of product of these numbers taken two at a time)
here, sum of ± 1, ± 2 , ± 3, ± 4... ± n =0
so sum of product of these numbers taken two at a time= – (sum of squares of all the terms)/2
but, sum of sqaures= (-1)^2+(1)^2+(-2)^2+(2)^2+.....+(-n)^2+n^2
=2(1^2+2^2+.....+n^2)
hence the final answer becomes
 – r=1n r^2
option C

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