Review of sums of infinite series

This week we haven’t been doing much but reviewing lessons from the beginning of school since finals are approaching. So Im going to do this blog on reviewing lesson 13-5, Sums of infinite series since this lesson is in our review packet!

Notes to know:

-Only geometrics where lrl < 1 have an infinite sum.

The sum formula for geometric is S= t1/1-r

-To find where an infinite geometric converges, set lrl < 1 and solve for x.

-To write a repeating decimal as a fraction, do this:

Whats repeating/place – 1

Examples:

1 1)      Find the sum of the infinite geometric series.

9-6+4-…

To find your R: -6/9= -2/3 , 4/-6= -2/3 (r=-2/3)

S=9/1 – (-2/3)= 9/1+2/3= 27/5

2 2)      For what values does the series converge?

1+ (x-2) + (x-2)^2 + (x-2)^3

l x-2 l < 1

-1 < x-2 < 1

Add 2 to each side and your answer is 1<x<3

3 3)      Repeating decimals: Write .454545.. as a rational number

45/100-1 = 45/99= 5/11