Sums of Integers, Squares & Cubes (Edexcel A-Level Further Mathematics): Flashcards

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Sums of Integers, Squares & Cubes
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Formula for ∑r=1nr\sum_{r=1}^n r

n(n+1)2\frac{n(n+1)}{2}

Formula for ∑r=1nr2\sum_{r=1}^n r^2

n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}

Formula for ∑r=1nr3\sum_{r=1}^n r^3

[n(n+1)2]2\left[\frac{n(n+1)}{2}\right]^2

How to split ∑(ar+br)\sum (a_r + b_r)

∑ar+∑br\sum a_r + \sum b_r

How to factor constant from ∑c⋅ar\sum c \cdot a_r

c∑arc \sum a_r

∑r=1nr3\sum_{r=1}^n r^3 equals what squared?

[∑r=1nr]2\left[\sum_{r=1}^n r\right]^2 or [n(n+1)2]2\left[\frac{n(n+1)}{2}\right]^2

Value of ∑r=110r2\sum_{r=1}^{10} r^2

385385

Value of ∑r=18r\sum_{r=1}^8 r

3636

Value of ∑r=15r3\sum_{r=1}^5 r^3

225225

Common mistake: ignoring what in weighted sums?

Coefficients

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