13-5

Okay, so this week I am going to teach you how to work infinite sum problems. They are very easy to learn how to do and are mostly algebra. But, first I am going to tell you a few things you are going to need know.

Notes:

• You can't find an infinite sum of an arithmetic series.
• Only geometric series where lrl < 1 have an infinite sum.
• The formula for these types of problems are S=t1/1-r
• When finding the infinite geometric converges, set lrl < 1 and solve for x.
• The last thing you need to know is, to write a repeating decimal as a fraction you would do what's repeating/place - 1

Okay, so now that you know all of that I am going to work a few examples for you. This should help you better understand what is going on.

Example 1: Write this repeating decimal as a fraction .23232323

• The number that is repeating is 23
• So you would put 23/100 -1
• You would put 100 - 1 becaue the 3 is in the 100ths place.
• So you would then get 23/99.
• And your answer is 23/99.

Example 2: Find the sum of the infinite geometric series.. 24-12+6-3+...

• You are going to use the formula I gave you above which is S=t1/1-r.
• S is what you are trying to find which is the sum.
• t1 is the first term given to you, which is 24
• r is the number that is being mulitplied to get the next number, which is (-1/2).
• So then you are going to plug into the formula.
• S= 24/1-(-1/2)
• Your answer is going to be S=16

Well that's it for this week. Byeeee

--Halie! :)