Standard +0.8 This requires recognizing the general term as r(r+1)(r+2), expanding to a cubic polynomial, then applying standard summation formulae for Σr, Σr², and Σr³. While the technique is standard for Further Maths, it involves multiple steps including algebraic manipulation and factorization, making it moderately challenging but still a routine Further Pure exercise.
1 Using standard summation of series formulae, determine the sum of the first \(n\) terms of the series \(( 1 \times 2 \times 4 ) + ( 2 \times 3 \times 5 ) + ( 3 \times 4 \times 6 ) + \ldots\),
where \(n\) is a positive integer. Give your answer in fully factorised form.
1 Using standard summation of series formulae, determine the sum of the first $n$ terms of the series $( 1 \times 2 \times 4 ) + ( 2 \times 3 \times 5 ) + ( 3 \times 4 \times 6 ) + \ldots$,\\
where $n$ is a positive integer. Give your answer in fully factorised form.
\hfill \mbox{\textit{OCR MEI Further Pure Core 2020 Q1 [6]}}