Chapter 3 · Test 1
Sequences, Series & Limits
Sequence limits, geometric series, convergence, and present value.
What you will learn
- Find a term of a geometric sequence
- Discount a future payment
- Sum a convergent geometric series
Reasoning habits that help
- The exponent is n − 1 because the first term contains zero applications of the common ratio.
- Discounting reverses compounding: future dollars are divided by the accumulated interest factor.
- An infinite geometric series converges exactly when the common ratio has absolute value below one.
Where economists use these methods
- Geometric sequences model compound growth in prices, output, population, debt, and investment balances.
- Present-value equations compare payments occurring at different dates in finance, policy, and cost-benefit analysis.
- Infinite geometric sums value perpetuities and repeated streams of discounted benefits or costs.