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in Binomial theorem by (46.6k points)

The sum of the products of every pair of the first n natural numbers is 

(a)  n(n + 1)(3n2 - n - 2)/24

(b)  n(n + 1)(3n2 + n + 2)/24

(c)  n(n - 1)(3n2 - n - 2)/24

(d)  None of these 

1 Answer

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Best answer

Correct option  (a)  n(n + 1)(3n2 - n - 2)/24

S = 1·2 + 1·3 + 1·4 + … + 2·3 + 2·4 + … + 3·4 + 3·5 + … + (n - 1)n. 

[1 + 2 + 3 + … (n - 1) + n]2 = 12 + 22 + 32 + … + (n - 1)2 + n2 + 2 (1·2 + 1·3 + 1·4 + … + 2·3 + 2·4 + … + 3·4 + … + (n - 1)n)

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