91Ó°ÊÓ

a. Write each series in sigma notation. b. Determine whether each sum increases without limit, decreases without limit, or approaches a finite limit. If the series has a finite limit, find that limit. \(5+1+\frac{1}{5}+\frac{1}{25}+\cdots\)

In \(3-8,\) determine if each sequence is an arithmetic sequence. If the sequence is arithmetic, find the common difference. $$ 20,15,10,5,0, \dots $$

In \(3-14 :\) a. Write each arithmetic series as the sum of terms. b. Find each sum. $$ \sum_{n=1}^{6} n^{3} $$

In \(3-14,\) find the sum of \(n\) terms of each geometric series. $$ a_{1}=10, r=10, n=6 $$

In \(3-8,\) find the sum of each series using the formula for the partial sum of an arithmetic series. Be sure to show your work. $$ 0+\frac{1}{3}+\frac{2}{3}+1+\frac{4}{3}+\frac{5}{3}+2 $$

In \(3-14 :\) a. Write each arithmetic series as the sum of terms. b. Find each sum. $$ \sum_{k=1}^{10}(100-5 k) $$

In \(3-18,\) write the first five terms of each sequence. $$ a_{n}=\frac{n}{2} $$

In \(3-14,\) determine whether each given sequence is geometric. If it is geometric, find \(r\) . If it is not geometric, explain why it is not. $$ 1,-3,9,-27,81, \dots $$

In \(3-8,\) determine if each sequence is an arithmetic sequence. If the sequence is arithmetic, find the common difference. $$ 1,2,4,8,16, \dots $$

In \(3-14,\) find the sum of \(n\) terms of each geometric series. $$ a_{3}=0.4, r=2, n=12 $$