Discussion questions
Choose a section to work through its questions and solutions. Your progress is shared across pages. Ranges follow collection order; original source labels are kept on each question.
Section 1 · Questions 1–6
From a recurrence to an explicit term · Observe an alternating convergent recurrence · +4 more
- Question 1 · From a recurrence to an explicit term
- Question 2 · Observe an alternating convergent recurrence
- Question 3 · Exclude a digit using arithmetic sums
- Question 4 · Sum increasing interest-free instalments
- Question 5 · Count a shared middle pearl once
- Question 6 · Recover geometric terms from partial sums
Section 2 · Questions 7–12
Bound the tail of a convergent geometric series · Compare arithmetic and geometric partial sums · +4 more
- Question 7 · Bound the tail of a convergent geometric series
- Question 8 · Compare arithmetic and geometric partial sums
- Question 9 · Split mixed sigma sums into arithmetic and geometric parts
- Question 10 · Change a summation range with two partial sums
- Question 11 · Deduce an infinite tail from a finite identity
- Question 12 · Reindex a rational series by two methods
Section 3 · Questions 13–18
Solve a daily retention recurrence · Find a positive fixed point and prove decrease above it · +4 more
- Question 13 · Solve a daily retention recurrence
- Question 14 · Find a positive fixed point and prove decrease above it
- Question 15 · Use a logarithmic fixed-point graph to compare terms
- Question 16 · Compare geometric and arithmetic instrument bars
- Question 17 · Combine a capped geometric plan with arithmetic increments
- Question 18 · Track beginning-of-month deposits and monthly interest