5.7&5.8 Day II: Arithmetic and Geometric Series.

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Presentation transcript:

5.7&5.8 Day II: Arithmetic and Geometric Series. By the end of class you will be able to calculate the sum of arithmetic and geometric series.

Gauss Punishment Problem Without a calculator find the sum of the natural numbers from 1 to100 Gauss finished this problem in less than a minute when 10 years old!

Series vs. Sequences Sequence: a collection of terms that follow a pattern/rule Series: the sum of terms of a sequence

Arithmetic Series

Find the following sums 1) 4, 7, 10, 13….if n = 50 2) The first 30 even natural numbers

The Salary Dilemma You are asked to work for the next 30 days at a fast food restaurant. Choose your salary from the following 2 choices: $100,000 for the month $.01 for day 1, $.02 for day 2, $.04 for day 3 etc.

Geometric Series

Find the following sums 2) The basketball bounce-original height = 60ft, sum of heights after 8 bounces.

Basketball problem extended Will the basketball ever stop bouncing? What will the final sum of basketball heights be?

E-Mail Junk You receive an e-mail from a friend and have to forward it to 7 of your friends to receive good luck. Those 7 friends forward it to 7 of their different friends. This process continues for 8 cycles. How many total e-mails are sent?

Summarizer Sequences and Series are alike because…. But different because….