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 are everywhere in mathematics! In these problems you can explore some sequences, learn how to represent them, and how to calculate sums of series.
Summats Clear Age 16 to 18Challenge Level 
Age 16 to 18
Challenge Level
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.
Be Reasonable Age 16 to 18Challenge Level
Age 16 to 18
Challenge Level
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
progression.
Harmonically Age 16 to 18Challenge Level
Age 16 to 18
Challenge Level
Is it true that a large integer m can be taken such that: 1 + 1/2 +
1/3 + ... +1/m > 100 ?