Advanced Problem Solving Module 23

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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.

Be Reasonable link

Be Reasonable 

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

Summats Clear link

Summats Clear 

Stage: 5 Challenge Level: Challenge Level:1

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.

Harmonically link

Harmonically 

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?

Sequences and Series link

Sequences and Series 

Challenge Level: Challenge Level:1

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.