Tag: Week 2

Week 2- Precalc 11

yil2016 on

This week we learned the geometric series, and I think the most interesting thing for me is to find the sum of the geometric series of infinite terms.There’s a formula for summation:s_{infinite}=\frac{a}{1-r}.However, before we use this formula we need to determine whether the geometric series is convergent or diverging.If the common ratio (r) of this series are greater than 1 or less than negative 1, it is diverging.We can not calculate the sum of diverging series.When the common ratio is between one and zero or between zero and negative one, the sum of this sequence can be calculated by the formula.

EX：

1)Find the sum of this geometric series :1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+…

r=\frac{1}{2},

s_{infinite}=\frac{a}{1-r}=\frac{1}{1-\frac{1}{2}}=2

 

2)Find the sum of this geometric series:1+5+10+50+…

r=5

So this sequence is diverging, you can’t find the sum of the infinite terms.