Summing Series and the Method of Differences (AQA A-Level Further Maths): Quizzes

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Summing Series and the Method of Differences
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What does r=1nur\sum_{r=1}^{n} u_r mean in sigma notation?

Sum of all terms from u1u_1 to unu_n

What is the formula for r=1nr\sum_{r=1}^{n} r?

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

What is the formula for r=1nr2\sum_{r=1}^{n} r^2?

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

What is the formula for r=1nr3\sum_{r=1}^{n} r^3?

n2(n+1)24\frac{n^2(n+1)^2}{4}

What elegant relationship exists between r3\sum r^3 and r\sum r?

r3=(r)2\sum r^3 = \left(\sum r\right)^2

When can the method of differences be used?

When ur=f(r+1)f(r)u_r = f(r+1) - f(r)

Using method of differences, r=1nur\sum_{r=1}^{n} u_r equals what if ur=f(r+1)f(r)u_r = f(r+1) - f(r)?

f(n+1)f(1)f(n+1) - f(1)

Are the three standard summation formulae provided in the exam formula booklet?

No, they must be memorised

What key technique helps identify cancellations in method of differences?

Writing differences vertically

What is uru_r called in sigma notation?

The general term

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