Standard +0.8 This is a Further Maths question requiring expansion of the general term n(n+1)² into a cubic polynomial, then applying standard summation formulae for Σn, Σn², and Σn³. While methodical, it involves multiple algebraic steps and careful manipulation beyond typical A-level Core content, placing it moderately above average difficulty.
Question 2:
2 | n n
=∑r(r+1)2 =∑(r3+2r2 +r)
r=1 r=1
n n n
=∑r3+2∑r2 +∑r
r=1 r=1 r=1
1 1 1
= n2(n+1)2 +2. n(n+1)(2n+1)+ n(n+1)
4 6 2
1
= n(n+1) ( 3n(n+1)+4(2n+1)+6 )
12
1 ( )
= n(n+1) 3n2 +11n+10
12
1
= n(n+1) ( n+2 )( 3n+5 )
12 | M1
A1
A1 | 1.1a
1.1
1.1 | Correct split of terms and use of formulae
Correct forms for each summation
Can be earned even if 2 is dropped
1 ( )
3n4 +14n3+21n2 +10n earns 2 marks
12
Fully factorised form for this mark
[3]