수열 전체 문제

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$6-2+\frac{2}{3}-\frac{2}{9}+\frac{2}{27}-\frac{2}{81}+\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$-4+2-1+\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$6+12+24+48+96+192+\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$5+15+45+135+405+1215+\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$1,024+512+256+128+64+32+\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$6,561+2187+729+243+81+27+\ldots$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{3}$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{6}$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{7}$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{2}$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{45}$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{27}$

Find the total effect on the economy of each government tax rebate to each household in order to stimulate the economy if each household will spend the indicated percent of the rebate in goods and services.

New grandparents decide to invest $\char36 100$ per month in an annuity for their grandchild. The account will pay $6\%$ interest per year which is compounded monthly (12 times a year). How much will be in the child’s account at their twenty-first birthday?

Berenice just got her first full-time job after graduating from college at age 30. She decided to invest $\char36 500$ per quarter in an IRA (an annuity). The interest on the annuity is $7\%$ which is compounded quarterly (4 times a year). How much will be in the Berenice’s account when she retires at age 65?

Alice wants to purchase a home in about five years. She is depositing $\char36 500$ a month into an annuity that earns $5\%$ per year that is compounded monthly (12 times a year). How much will Alice have for her down payment in five years?

Myra just got her first full-time job after graduating from college. She plans to get a master’s degree, and so is depositing $\char36 2,500$ a year from her year-end bonus into an annuity. The annuity pays $6.5\%$ per year and is compounded yearly. How much will she have saved in five years to pursue her master’s degree?

Write the First Few Terms of a Sequence

In the following exercises, write the first five terms of the sequence whose general term is given.

${a}_{n}=7n-5$