91Ó°ÊÓ

In Exercises 113-116, find the indicated partial sum of the series. \( \displaystyle \sum_{i=1}^{\infty} 2 \left(\dfrac{1}{3} \right)^i \) Fifth partial sum

The sum of the first \( n \) terms of anarithmetic sequence with first term \( a_1 \) and common difference \( d \) is \( S_n \) Determine the sum if each term is increased by \( 5 \). Explain

In Exercises 113-116, find the indicated partial sum of the series. \( \displaystyle \sum_{n=1}^{\infty} 4 \left(-\dfrac{1}{2} \right)^n \) Third partial sum

A principal of \(\$ 2500\) is invested at 2\(\%\) interest. Find the amount after 20 years if the interest is compounded (a) annually, (b) semiannually, (c) quarterly, (d) monthly, and (e) daily.

A tool and die company buys a machine for \(\$ 175,000\) and it depreciates at a rate of 30\(\%\) per year. In other words, at the end of each year the depreciated value is 70\(\%\) of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.

In Exercises 113-116, find the indicated partial sum of the series. \( \displaystyle \sum_{n=1}^{\infty} 8 \left(-\dfrac{1}{4} \right)^n \) Fourth partial sum

A deposit of \( \$100 \) is made at the beginning of each month in an account that pays \( 6\% \) interest, compounded monthly. The balance \( A \) in the account at the end of \( 5 \) years is \( A = 100 \left(1 + \dfrac{0.06}{12}\right)^1 + \cdots + 100\left(1 + \dfrac{0.06}{12}\right)^{60} \) Find \( A \).

Exercises 117-120, find the sum of the infinite series. \( \displaystyle \sum_{i=1}^{\infty} 6 \left(\frac{1}{10} \right)^i \)

A deposit of \(50 is made at the beginning of each month in an account that pays 8% interest, compounded monthly. The balance \) A \( in the account at the end of 5 years is \) A = 50 \left(1 + \dfrac{0.08}{12}\right)^1 + \cdots + 50\left(1 + \dfrac{0.06}{12}\right)^{60} \( Find \) A $.

Exercises 117-120, find the sum of the infinite series. \( \displaystyle \sum_{k=1}^{\infty} \left(\frac{1}{10} \right)^k \)