ECON 1530 Lecture Notes - Lecture 4: Discounting, Decision Rule, Convergent Series

• School: York University
• Department: Economics
• Course: ECON 1530
• Professor: Chowdhury S Mahmoud

Document Summary

Suppose you have a sequence and create a new sequence by summing the rst n terms: Sn = a1 + a2 + a3 an. This is a special sequence we call a series. Series have many applications for nite and in nite n. A rm has revenue, (r), of $ 100 million. Calculate the total revenue, (tr), over the next ten years if the revenue increases by 10% a year. T r(n) = 100 + 100 1. 16 + 100 (1. 16)2 + + 100 (1. 16)n 1. T r(10) = 100 + 100 1. 16 + 100 (1. 16)2 + + 100 (1. 16)9. Sn = a + ak + ak2 + + akn 1 which is a nite geometric series with quotient k. Sn = a + ak + ak2 + + akn 2 + akn 1 ksn = ak + ak2 + ak3 + + akn 1 + akn.