Series, inverse cube, binomial coefficients, inequalities, sum of series, infinite sum.
[STEP III 2017 Question 1 (Pure)]
Underground Mathematics: Selected worked STEP questions
STEP Question database
University of Cambridge Mathematics Faculty: What do we look for?
University of Cambridge Mathematics Faculty: Information about STEP
University of Cambridge Admissions Office: Undergraduate course information for Mathematics
Stephen Siklos' "Advanced Problems in Mathematics" book (external link)
MEI: Worked solutions to STEP questions (external link)
OCR: Exam board information about STEP (external link)