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Advanced Problem Solving Module 23
Summing series comes up in many STEP and other advanced mathematics examinations questions, so it's important to be familiar with the key concepts. This module offers some reminders and practice.
Sequences and Series
Sequences are everywhere in mathematics! In these problems you can explore some sequences, learn how to represent them, and how to calculate sums of series.
16 to 18
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
16 to 18
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
16 to 18
Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
Prepare for University - Pure Mathematics
Prepare for University - Applied Mathematics
NRICH and Olympiads