Question

The sum of all the products of the first n natural numbers taken two at a time is

• A. $\frac { 1 } { 24 }$n (n –1) (n + 1) (3n + 2)
• B. (n –1) (n –2)
• C. $\frac { 1 } { 6 }$n (n + 1) (n + 2) (n + 5)
• D. None of these

Answer 1

Answer: (A)

$\frac { 1 } { 24 }$n (n –1) (n + 1) (3n + 2)

Answer 2

We know that = (1 + 2 + ……+ n)²

=

̃ =$\frac { 1 } { 2 }$

= $\frac { \mathrm { n } } { 24 }$ (n –1) (n + 1) (3n + 2)