Notes
Series
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nΣ1 r = 1/2n(n+1)
nΣ1 r^2 = 1/6n(n+1)(2n+1)
nΣ1 r^3 = 1/4n^2(n+1)^2
nΣ1 (2r^3 + r) = nΣ12r^3 + nΣ1 r = 2(0.25(n)^2(n+1)^2) + 0.5(n)(n+1)
=> 0.5(n^2)(n+1)^2 + 0.5(n)(n+1)
=> (n+1)^2 = (n+1)(n+1) = n^2 + 2n + 1
=> 0.5(n^2 + 2n + 1)(n^2) + 0.5(n)(n+1)
=> 0.5(n^4 + 2n^3 + n^2) + 0.5(n^2 + n)
=> (n^4/2 + n^3 + n^2/2) + (n^2/2 + n/2)
=> n^4/2 + n^3 + n^2 + n/2
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- A2 Further Mathematics (Further Pure 1) Note on Series, created by Sirius Hall on 08/02/2017.
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- Sirius Hall
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