91Ó°ÊÓ

Evaluate each infinite series, if possible. $$\sum_{j=0}^{\infty} 5 \cdot\left(\frac{1}{10}\right)^{j}$$

Suppose your salary is \(\$ 45,000\) and you receive a \(\$ 1,500\) raise for each year you work for 35 years. a. How much will you earn during the 35th year? b. What is the total amount you earned over your 35 -year career?

A college freshman decides to stop ordering late-night pizzas (for both health and cost reasons). He realizes that he has been spending \(\$ 50\) a week on pizzas. Instead, he deposits \(\$ 50\) into an account that compounds weekly and pays \(4 \%\) interest. (Assume 52 weeks annually.) How much money will be in the account after 52 weeks?

Dr. Schober contributes \(\$ 500\) from her paycheck (weekly) to a tax-deferred investment account. Assuming the investment earns \(6 \%\) and is compounded weekly, how much will be in the account after 26 weeks? 52 weeks?

In calculus, the difference quotient \(\frac{f(x+h)-f(x)}{h}\) of a function \(f\) is used to find the derivative of the function \(f\). Use the Binomial theorem to find the difference quotient of each function. $$f(x)=x^{n}$$

Mathematics. Find the exact sum of $$ \frac{1}{e}+\frac{3}{e}+\frac{5}{e}+\dots+\frac{23}{e} $$

Evaluate each infinite series, if possible. $$\sum_{j=0}^{\infty} 1^{j}$$

In calculus, the difference quotient \(\frac{f(x+h)-f(x)}{h}\) of a function \(f\) is used to find the derivative of the function \(f\). Use the Binomial theorem to find the difference quotient of each function. $$f(x)=(2 x)^{n}$$

If a new graduate decides she wants to save for a house and she is able to put \(\$ 300\) every month into an account that earns \(5 \%\) compounded monthly, how much will she have in the account after 5 years?

Explain the mistake that is made. Find the general, or \(n\) th, term of the arithmetic sequence \(3,4,5,6,7, \dots\) Solution: The common difference of this sequence is 1 \(d=1\) The first term is \(3 . \quad a_{1}=3\) The general term is \(a_{n}=a_{1}+n d . \quad a_{n}=3+n\) This is incorrect. What mistake was made?