CAIE A-Level Further Math AS 1.3.1 Standard Series Sums Questions

Practise using standard summation formulae to simplify arithmetic and polynomial series.

Exam points

apply standard formulae for series sums
simplify polynomial and arithmetic summations
solve standard series sum problems in context

[Maximum number: 3]

Given that $\sum_{r=1}^{n}(r+a)=n$ , find a in terms of n.

$\sum_{r=1}^{n}(r+a)=\sum_{r=1}^{n} r+a n$
Relates with $\sum r$ .

$\frac{1}{2} n(n+1)+a n=n$
Applies $\sum_{r=1}^{n} r=\frac{1}{2} n(n+1)$ .

$a=\frac{1}{2}(1-n)$
3

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CAIE A-Level Further Math AS 1.3.1 Standard Series Sums Questions question 1