Challenging +1.2 This is a Further Maths question requiring identification of the general term r(r+1)(r+3), expansion to a cubic in r, then application of standard summation formulae. While it involves multiple steps and algebraic manipulation, it's a fairly standard exercise in using Σr, Σr², Σr³ formulae with straightforward pattern recognition and no novel insight required.
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. [6]
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. [6]
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q4 [6]}}