Let the sum ∑ n = 1 9 1 n ( n + 1 ) ( n + 2 ) , written in the rational form be p q (where p and q are co-prime), then the value of q - p 10 is, (where [.] is the greatest integer function)

Question

Let the sum &#x2211; n = 1 9 1 n ( n + 1 ) ( n + 2 ) , written in the rational form be p q (where p and q are co-prime), then the value of q - p 10 is, (where [.] is the greatest integer function)

Quantrex Academy · Accepted Answer

Correct answer: 8

∑ n = 1 9 1 2 n + 2 - n n n + 1 n + 2 = 1 2 1 1.2 - 1 2.3 + 1 2.3 - 1 3.4 + … + 1 9 × 10 - 1 10 × 11 = 1 2 1 2 - 1 110 = 1 2 55 - 1 110 = 27 110 ⇒ q - p = 110 - 27 = 83

Let the sum ∑ n = 1 9 1 n ( n + 1 ) ( n + 2 ) , written in the rational form be p q (where p and q are co-prime), then the value of q - p 10 is, (where [.] is the greatest integer function)

Correct answer

Step-by-step solution

More from Sequences and Series

Let the sum &#x2211; n = 1 9 1 n ( n + 1 ) ( n + 2 ) , written in the rational form be p q (where p and q are co-prime), then the value of q - p 10 is, (where [.] is the greatest integer function)

Correct answer

Step-by-step solution

More from Sequences and Series

Let the sum ∑ n = 1 9 1 n ( n + 1 ) ( n + 2 ) , written in the rational form be p q (where p and q are co-prime), then the value of q - p 10 is, (where [.] is the greatest integer function)