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Chapter 10: Problem 10
Write the first five terms of the sequence. $$ a_{n}=5-\frac{1}{n}+\frac{1}{n^{2}} $$
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Annuity A deposit of 100 dollars is made at the beginning of each month for 5 years in an account that pays \(10 \%\) interest, compounded monthly. Use a symbolic algebra utility to find the balance \(A\) in the account at the end of the 5 years. $$A=100\left(1+\frac{0.10}{12}\right)+\cdots+100\left(1+\frac{0.10}{12}\right)^{60}$$
Determine the convergence or divergence of the series. Use a symbolic algebra utility to verify your result. $$ \sum_{n=1}^{\infty} \frac{n+1}{2 n-1} $$
Individual Retirement Account A deposit of 2000 dollars is made each year in an account that earns \(11 \%\) interest compounded annually. The balance after \(n\) years is given by \(A_{n}=2000(11)\left[(1.1)^{n}-1\right] .\) (a) Compute the first six terms of the sequence. (b) Find the balance after 20 years by finding the 20 th term of the sequence. (c) Use a symbolic algebra utility to find the balance after 40 years by finding the 40 th term of the sequence.
Write the next two terms of the arithmetic sequence. Describe the pattern you used to find these terms. $$ 2,5,8,11, \dots $$
Salary You accept a job that pays a salary of 40,000 dollars the first year. During the next 39 years, you will receive a \(4 \%\) raise each year. What would be your total compensation over the 40 -year period?
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