Session 9: Summing series

UCL Online STEP and AEA Preparation Sessions
Session 9: Summing series
General knowledge about summing series such as the formula for the sum of the
first n whole numbers; the formula for the sum of the squares of the first n whole
numbers; arithmetic and geometric series can be useful in STEP and AEA problems.
This knowledge combines with topics already covered to enable you to answer
questions like
What is the least value of n for which the sum of the first n terms of the arithmetic
progression 5, 12, 19, 26, ..... is greater than 10000 ?
Confidence with sigma notation is important in this topic as is being able to work
algebraically with factorial expressions and binomial coefficients.
It can be useful to find upper and lower bounds for summations by comparing them
to other summations whose value you can calculate more easily.
Summations arise when approximating the area under a curve using rectangles.
In this lecture we’ll look at examples of all of the above.
Example problem
The first and second terms of an arithmetic series are 100 and 95 respectively. The sum to n
terms of the series is Sn. Find the largest positive value of Sn.